Tropicalizations

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Effective Faithful Tropicalizations Associated to Linear Systems on Curves

Author : Shu Kawaguchi
Publisher : American Mathematical Soc.
ISBN 13 : 1470447533
Total Pages : 110 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Effective Faithful Tropicalizations Associated to Linear Systems on Curves by : Shu Kawaguchi

Download or read book Effective Faithful Tropicalizations Associated to Linear Systems on Curves written by Shu Kawaguchi and published by American Mathematical Soc.. This book was released on 2021-07-21 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a connected smooth projective curve X of genus g, global sections of any line bundle L with deg(L) ≥ 2g + 1 give an embedding of the curve into projective space. We consider an analogous statement for a Berkovich skeleton in nonarchimedean geometry: We replace projective space by tropical projective space, and an embedding by a homeomorphism onto its image preserving integral structures (or equivalently, since X is a curve, an isometry), which is called a faithful tropicalization. Let K be an algebraically closed field which is complete with respect to a nontrivial nonarchimedean value. Suppose that X is defined over K and has genus g ≥ 2 and that Γ is a skeleton (that is allowed to have ends) of the analytification Xan of X in the sense of Berkovich. We show that if deg(L) ≥ 3g − 1, then global sections of L give a faithful tropicalization of Γ into tropical projective space. As an application, when Y is a suitable affine curve, we describe the analytification Y an as the limit of tropicalizations of an effectively bounded degree.

Tropicalizations

Author : Frances R. Aparicio
Publisher : Dartmouth College Press
ISBN 13 :
Total Pages : 248 pages
Book Rating : 4.A/5 ( download)

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Book Synopsis Tropicalizations by : Frances R. Aparicio

Download or read book Tropicalizations written by Frances R. Aparicio and published by Dartmouth College Press. This book was released on 1997 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new conceptual lexicon challenges the colonizing discourses that traditionally represent Latinas/os.

Tropicalizations

Author : Frances R. Aparicio
Publisher : Dartmouth College Press
ISBN 13 :
Total Pages : 248 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis Tropicalizations by : Frances R. Aparicio

Nonarchimedean and Tropical Geometry

Author : Matthew Baker
Publisher : Springer
ISBN 13 : 3319309455
Total Pages : 534 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Nonarchimedean and Tropical Geometry by : Matthew Baker

Download or read book Nonarchimedean and Tropical Geometry written by Matthew Baker and published by Springer. This book was released on 2016-08-18 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume grew out of two Simons Symposia on "Nonarchimedean and tropical geometry" which took place on the island of St. John in April 2013 and in Puerto Rico in February 2015. Each meeting gathered a small group of experts working near the interface between tropical geometry and nonarchimedean analytic spaces for a series of inspiring and provocative lectures on cutting edge research, interspersed with lively discussions and collaborative work in small groups. The articles collected here, which include high-level surveys as well as original research, mirror the main themes of the two Symposia. Topics covered in this volume include: Differential forms and currents, and solutions of Monge-Ampere type differential equations on Berkovich spaces and their skeletons; The homotopy types of nonarchimedean analytifications; The existence of "faithful tropicalizations" which encode the topology and geometry of analytifications; Relations between nonarchimedean analytic spaces and algebraic geometry, including logarithmic schemes, birational geometry, and the geometry of algebraic curves; Extended notions of tropical varieties which relate to Huber's theory of adic spaces analogously to the way that usual tropical varieties relate to Berkovich spaces; and Relations between nonarchimedean geometry and combinatorics, including deep and fascinating connections between matroid theory, tropical geometry, and Hodge theory.

Tropical and Logarithmic Methods in Enumerative Geometry

Author : Renzo Cavalieri
Publisher : Springer Nature
ISBN 13 : 3031394011
Total Pages : 163 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Tropical and Logarithmic Methods in Enumerative Geometry by : Renzo Cavalieri

Download or read book Tropical and Logarithmic Methods in Enumerative Geometry written by Renzo Cavalieri and published by Springer Nature. This book was released on 2023-11-01 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the lectures given at the Oberwolfach Seminar held in Fall 2021. Logarithmic Gromov-Witten theory lies at the heart of modern approaches to mirror symmetry, but also opens up a number of new directions in enumerative geometry of a more classical flavour. Tropical geometry forms the calculus through which calculations in this subject are carried out. These notes cover the foundational aspects of this tropical calculus, geometric aspects of the degeneration formula for Gromov-Witten invariants, and the practical nuances of working with and enumerating tropical curves. Readers will get an assisted entry route to the subject, focusing on examples and explicit calculations.

Analysis Meets Geometry

Author : Mats Andersson
Publisher : Birkhäuser
ISBN 13 : 3319524712
Total Pages : 464 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Analysis Meets Geometry by : Mats Andersson

Download or read book Analysis Meets Geometry written by Mats Andersson and published by Birkhäuser. This book was released on 2017-09-04 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to the memory of Mikael Passare, an outstanding Swedish mathematician who devoted his life to developing the theory of analytic functions in several complex variables and exploring geometric ideas first-hand. It includes several papers describing Mikael’s life as well as his contributions to mathematics, written by friends of Mikael’s who share his attitude and passion for science. A major section of the book presents original research articles that further develop Mikael’s ideas and which were written by his former students and co-authors. All these mathematicians work at the interface of analysis and geometry, and Mikael’s impact on their research cannot be underestimated. Most of the contributors were invited speakers at the conference organized at Stockholm University in his honor. This book is an attempt to express our gratitude towards this great mathematician, who left us full of energy and new creative mathematical ideas.

Algebraic and Combinatorial Aspects of Tropical Geometry

Author : Erwan Brugalle
Publisher : American Mathematical Soc.
ISBN 13 : 0821891464
Total Pages : 363 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic and Combinatorial Aspects of Tropical Geometry by : Erwan Brugalle

Download or read book Algebraic and Combinatorial Aspects of Tropical Geometry written by Erwan Brugalle and published by American Mathematical Soc.. This book was released on 2013-05-23 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the CIEM workshop on Tropical Geometry, held December 12-16, 2011, at the International Centre for Mathematical Meetings (CIEM), Castro Urdiales, Spain. Tropical geometry is a new and rapidly developing field of mat

Essentials of Tropical Combinatorics

Author : Michael Joswig
Publisher : American Mathematical Society
ISBN 13 : 1470466538
Total Pages : 398 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Essentials of Tropical Combinatorics by : Michael Joswig

Download or read book Essentials of Tropical Combinatorics written by Michael Joswig and published by American Mathematical Society. This book was released on 2021-12-08 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. Building bridges between these two subject areas is fruitful in two ways. Through tropical geometry optimization algorithms become applicable to questions in algebraic geometry. Conversely, looking at topics in optimization through the tropical geometry lens adds an additional layer of structure. The author covers contemporary research topics that are relevant for applications such as phylogenetics, neural networks, combinatorial auctions, game theory, and computational complexity. This self-contained book grew out of several courses given at Technische Universität Berlin and elsewhere, and the main prerequisite for the reader is a basic knowledge in polytope theory. It contains a good number of exercises, many examples, beautiful figures, as well as explicit tools for computations using $texttt{polymake}$.

Introduction to Tropical Geometry

Author : Diane Maclagan
Publisher : American Mathematical Society
ISBN 13 : 1470468565
Total Pages : 363 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Introduction to Tropical Geometry by : Diane Maclagan

Download or read book Introduction to Tropical Geometry written by Diane Maclagan and published by American Mathematical Society. This book was released on 2021-12-13 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of the six chapters concludes with problems that will help the readers to practice their tropical skills, and to gain access to the research literature. This wonderful book will appeal to students and researchers of all stripes: it begins at an undergraduate level and ends with deep connections to toric varieties, compactifications, and degenerations. In between, the authors provide the first complete proofs in book form of many fundamental results in the subject. The pages are sprinkled with illuminating examples, applications, and exercises, and the writing is lucid and meticulous throughout. It is that rare kind of book which will be used equally as an introductory text by students and as a reference for experts. —Matt Baker, Georgia Institute of Technology Tropical geometry is an exciting new field, which requires tools from various parts of mathematics and has connections with many areas. A short definition is given by Maclagan and Sturmfels: “Tropical geometry is a marriage between algebraic and polyhedral geometry”. This wonderful book is a pleasant and rewarding journey through different landscapes, inviting the readers from a day at a beach to the hills of modern algebraic geometry. The authors present building blocks, examples and exercises as well as recent results in tropical geometry, with ingredients from algebra, combinatorics, symbolic computation, polyhedral geometry and algebraic geometry. The volume will appeal both to beginning graduate students willing to enter the field and to researchers, including experts. —Alicia Dickenstein, University of Buenos Aires, Argentina

Tropical and Idempotent Mathematics

Author : Grigoriĭ Lazarevich Litvinov
Publisher : American Mathematical Soc.
ISBN 13 : 0821847821
Total Pages : 395 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Tropical and Idempotent Mathematics by : Grigoriĭ Lazarevich Litvinov

Download or read book Tropical and Idempotent Mathematics written by Grigoriĭ Lazarevich Litvinov and published by American Mathematical Soc.. This book was released on 2009 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of papers from the International Conference on Tropical and Idempotent Mathematics, held in Moscow, Russia in August 2007. This is a relatively new branch of mathematical sciences that has been rapidly developing and gaining popularity over the last decade. Tropical mathematics can be viewed as a result of the Maslov dequantization applied to 'traditional' mathematics over fields. Importantly, applications in econophysics and statistical mechanics lead to an explanation of the nature of financial crises. Another original application provides an analysis of instabilities in electrical power networks. Idempotent analysis, tropical algebra, and tropical geometry are the building blocks of the subject. Contributions to idempotent analysis are focused on the Hamilton-Jacobi semigroup, the max-plus finite element method, and on the representations of eigenfunctions of idempotent linear operators. Tropical algebras, consisting of plurisubharmonic functions and their germs, are examined. The volume also contains important surveys and research papers on tropical linear algebra and tropical convex geometry.

Tropical and Non-Archimedean Geometry

Author : Omid Amini
Publisher : American Mathematical Soc.
ISBN 13 : 1470410214
Total Pages : 274 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Tropical and Non-Archimedean Geometry by : Omid Amini

Download or read book Tropical and Non-Archimedean Geometry written by Omid Amini and published by American Mathematical Soc.. This book was released on 2014-12-26 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past decade, it has become apparent that tropical geometry and non-Archimedean geometry should be studied in tandem; each subject has a great deal to say about the other. This volume is a collection of articles dedicated to one or both of these disciplines. Some of the articles are based, at least in part, on the authors' lectures at the 2011 Bellairs Workshop in Number Theory, held from May 6-13, 2011, at the Bellairs Research Institute, Holetown, Barbados. Lecture topics covered in this volume include polyhedral structures on tropical varieties, the structure theory of non-Archimedean curves (algebraic, analytic, tropical, and formal), uniformisation theory for non-Archimedean curves and abelian varieties, and applications to Diophantine geometry. Additional articles selected for inclusion in this volume represent other facets of current research and illuminate connections between tropical geometry, non-Archimedean geometry, toric geometry, algebraic graph theory, and algorithmic aspects of systems of polynomial equations.

Tropical Geometry and Integrable Systems

Author : Chris Athorne
Publisher : American Mathematical Soc.
ISBN 13 : 0821875531
Total Pages : 170 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Tropical Geometry and Integrable Systems by : Chris Athorne

Download or read book Tropical Geometry and Integrable Systems written by Chris Athorne and published by American Mathematical Soc.. This book was released on 2012 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference on tropical geometry and integrable systems, held July 3-8, 2011, at the University of Glasgow, United Kingdom. One of the aims of this conference was to bring together researchers in the field of tropical geometry and its applications, from apparently disparate ends of the spectrum, to foster a mutual understanding and establish a common language which will encourage further developments of the area. This aim is reflected in these articles, which cover areas from automata, through cluster algebras, to enumerative geometry. In addition, two survey articles are included which introduce ideas from researchers on one end of this spectrum to researchers on the other. This book is intended for graduate students and researchers interested in tropical geometry and integrable systems and the developing links between these two areas.

On Tropical Grounds

Author : Francisco-J. Hernandez Adrian
Publisher : John Wiley & Sons
ISBN 13 : 1509561684
Total Pages : 293 pages
Book Rating : 4.5/5 (95 download)

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Book Synopsis On Tropical Grounds by : Francisco-J. Hernandez Adrian

Download or read book On Tropical Grounds written by Francisco-J. Hernandez Adrian and published by John Wiley & Sons. This book was released on 2024-10-11 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: On Tropical Grounds develops a new approach to the avant-garde and Surrealism in Caribbean and Atlantic studies. The book examines how islands and their tropical associations figure in the cultural and political imaginaries of the Caribbean and the Atlantic, and identifies genealogies of local responses to continental fantasies of exotic insularity. Examining written and visual works that reflect on the Hispanic and Francophone Caribbean and the Canary Islands, as well as critical debates around discourses of insularity in island and metropolitan spaces, this book considers notions of ethnic purity, originality, imitation, appropriation, cosmopolitanism, and self-exoticism to challenge the idea that avant-garde practices were pre-eminently urban and metropolitan cultural forms. The book argues that attention to the relational dimension implicit in exchanges around ideas of anticolonial struggle, radical social transformation, and anti-fascist resistance should inform analyses of cultural production in Caribbean and Atlantic insular spaces. On Tropical Grounds develops a persuasive critical model for the investigation of politically and aesthetically situated archipelagic relations that transgresses disciplinary boundaries and reconfigures our conception of the avant-garde as a global movement that was overdetermined by racial, gender, and colonial conflicts. This book will be of value to anyone interested in Caribbean and Atlantic studies, avant-garde and visual culture studies, and literary and cultural studies.

Tropical Visions in an Age of Empire

Author : Felix Driver
Publisher : University of Chicago Press
ISBN 13 : 0226164705
Total Pages : 292 pages
Book Rating : 4.2/5 (261 download)

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Book Synopsis Tropical Visions in an Age of Empire by : Felix Driver

Download or read book Tropical Visions in an Age of Empire written by Felix Driver and published by University of Chicago Press. This book was released on 2010-11-15 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contrast between the temperate and the tropical is one of the most enduring themes in the history of the Western geographical imagination. Caught between the demands of experience and representation, documentation and fantasy, travelers in the tropics have often treated tropical nature as a foil to the temperate, to all that is civilized, modest, and enlightened. Tropical Visions in an Age of Empire explores images of the tropical world—maps, paintings, botanical drawings, photographs, diagrams, and texts—produced by European and American travelers over the past three centuries. Bringing together a group of distinguished contributors from disciplines across the arts and humanities, this volume contains eleven beautifully illustrated essays—arranged in three sections devoted to voyages, mappings, and sites—that consider the ways that tropical places were encountered, experienced, and represented in visual form. Covering a wide range of tropical sites in the Pacific, South Asia, West Africa, the Caribbean, and Latin America, the book will appeal to a broad readership: scholars of postcolonial studies, art history, literature, imperial history, history of science, geography, and anthropology.

Tropical Gothic in Literature and Culture

Author : Justin D. Edwards
Publisher : Routledge
ISBN 13 : 1317425782
Total Pages : 275 pages
Book Rating : 4.3/5 (174 download)

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Book Synopsis Tropical Gothic in Literature and Culture by : Justin D. Edwards

Download or read book Tropical Gothic in Literature and Culture written by Justin D. Edwards and published by Routledge. This book was released on 2016-01-13 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tropical Gothic examines Gothic within a specific geographical area of ‘the South’ of the Americas. In so doing, we structure the book around geographical coordinates (from North to South) and move between various national traditions of the gothic (Mexico, Argentina, Brazil, etc) alongside regional manifestations of the Gothic (the US south and the Caribbean) as well as transnational movements of the Gothic within the Americas. The reflections on national traditions of the Gothic in this volume add to the critical body of literature on specific languages or particular nations, such as Scottish Gothic, American Gothic, Canadian Gothic, German Gothic, Kiwi Gothic, etc. This is significant because, while the Southern Gothic in the US has been thoroughly explored, there is a gap in the critical literature about the Gothic in the larger context of region of ‘the South’ in the Americas. This volume does not pretend to be a comprehensive examination of tropical Gothic in the Americas; rather, it pinpoints a variety of locations where this form of the Gothic emerges. In so doing, the transnational interventions of the Gothic in this book read the flows of Gothic forms across borders and geographical regions to tease out the complexities of Gothic cultural production within cultural and linguistic translations. Tropical Gothic includes, but is by no means limited to, a reflection on a region where European colonial powers fought intensively against indigenous populations and against each other for control of land and resources. In other cases, the vast populations of African slaves were transported, endowing these regions with a cultural inheritance that all the nations involved are still trying to comprehend. The volume reflects on how these histories influence the Gothic in this region.

New York Ricans from the Hip Hop Zone

Author : R. Rivera
Publisher : Springer
ISBN 13 : 1403981671
Total Pages : 285 pages
Book Rating : 4.4/5 (39 download)

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Book Synopsis New York Ricans from the Hip Hop Zone by : R. Rivera

Download or read book New York Ricans from the Hip Hop Zone written by R. Rivera and published by Springer. This book was released on 2003-02-07 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: New York Puerto Ricans have been an integral part of hip hop culture since day one: from 1970s pioneers like Rock Steady Crew's Jo-Jo, to recent rap mega-stars Big Punisher (R.I.P.) and Angie Martinez. Yet, Puerto Rican participation and contributions to hip hop have often been downplayed and even completely ignored. And when their presence has been acknowledged, it has frequently been misinterpreted as a defection from Puerto Rican culture and identity, into the African American camp. But nothing could be further from the truth. Through hip hop, Puerto Ricans have simply stretched the boundaries of Puerto Ricanness and latinidad.

Facets of Algebraic Geometry: Volume 2

Author : Paolo Aluffi
Publisher : Cambridge University Press
ISBN 13 : 1108890547
Total Pages : 396 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Facets of Algebraic Geometry: Volume 2 by : Paolo Aluffi

Download or read book Facets of Algebraic Geometry: Volume 2 written by Paolo Aluffi and published by Cambridge University Press. This book was released on 2022-04-07 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written to honor the 80th birthday of William Fulton, the articles collected in this volume (the second of a pair) present substantial contributions to algebraic geometry and related fields, with an emphasis on combinatorial algebraic geometry and intersection theory. Featured include commutative algebra, moduli spaces, quantum cohomology, representation theory, Schubert calculus, and toric and tropical geometry. The range of these contributions is a testament to the breadth and depth of Fulton's mathematical influence. The authors are all internationally recognized experts, and include well-established researchers as well as rising stars of a new generation of mathematicians. The text aims to stimulate progress and provide inspiration to graduate students and researchers in the field.