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Chow Rings Decomposition Of The Diagonal And The Topology Of Families Am 187
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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.
Book Synopsis Trends in Contemporary Mathematics by : Vincenzo Ancona
Download or read book Trends in Contemporary Mathematics written by Vincenzo Ancona and published by Springer. This book was released on 2014-08-27 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topics faced in this book cover a large spectrum of current trends in mathematics, such as Shimura varieties and the Lang lands program, zonotopal combinatorics, non linear potential theory, variational methods in imaging, Riemann holonomy and algebraic geometry, mathematical problems arising in kinetic theory, Boltzmann systems, Pell's equations in polynomials, deformation theory in non commutative algebras. This work contains a selection of contributions written by international leading mathematicians who were speakers at the "INdAM Day", an initiative born in 2004 to present the most recent developments in contemporary mathematics.
Book Synopsis Chow Rings, Decomposition of the Diagonal, and the Topology of Families by : Claire Voisin
Download or read book Chow Rings, Decomposition of the Diagonal, and the Topology of Families written by Claire Voisin and published by Princeton University Press. This book was released on 2014-02-23 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Claire Voisin provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. The volume is intended for both students and researchers, and not only presents a survey of the geometric methods developed in the last thirty years to understand the famous Bloch-Beilinson conjectures, but also examines recent work by Voisin. The book focuses on two central objects: the diagonal of a variety—and the partial Bloch-Srinivas type decompositions it may have depending on the size of Chow groups—as well as its small diagonal, which is the right object to consider in order to understand the ring structure on Chow groups and cohomology. An exploration of a sampling of recent works by Voisin looks at the relation, conjectured in general by Bloch and Beilinson, between the coniveau of general complete intersections and their Chow groups and a very particular property satisfied by the Chow ring of K3 surfaces and conjecturally by hyper-Kähler manifolds. In particular, the book delves into arguments originating in Nori's work that have been further developed by others.
Book Synopsis 3264 and All That by : David Eisenbud
Download or read book 3264 and All That written by David Eisenbud and published by Cambridge University Press. This book was released on 2016-04-14 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: 3264, the mathematical solution to a question concerning geometric figures.
Book Synopsis Lectures on K3 Surfaces by : Daniel Huybrechts
Download or read book Lectures on K3 Surfaces written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2016-09-26 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.
Book Synopsis Lecture Notes on Motivic Cohomology by : Carlo Mazza
Download or read book Lecture Notes on Motivic Cohomology written by Carlo Mazza and published by American Mathematical Soc.. This book was released on 2006 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of a motive is an elusive one, like its namesake "the motif" of Cezanne's impressionist method of painting. Its existence was first suggested by Grothendieck in 1964 as the underlying structure behind the myriad cohomology theories in Algebraic Geometry. We now know that there is a triangulated theory of motives, discovered by Vladimir Voevodsky, which suffices for the development of a satisfactory Motivic Cohomology theory. However, the existence of motives themselves remains conjectural. This book provides an account of the triangulated theory of motives. Its purpose is to introduce Motivic Cohomology, to develop its main properties, and finally to relate it to other known invariants of algebraic varieties and rings such as Milnor K-theory, etale cohomology, and Chow groups. The book is divided into lectures, grouped in six parts. The first part presents the definition of Motivic Cohomology, based upon the notion of presheaves with transfers. Some elementary comparison theorems are given in this part. The theory of (etale, Nisnevich, and Zariski) sheaves with transfers is developed in parts two, three, and six, respectively. The theoretical core of the book is the fourth part, presenting the triangulated category of motives. Finally, the comparison with higher Chow groups is developed in part five. The lecture notes format is designed for the book to be read by an advanced graduate student or an expert in a related field. The lectures roughly correspond to one-hour lectures given by Voevodsky during the course he gave at the Institute for Advanced Study in Princeton on this subject in 1999-2000. In addition, many of the original proofs have been simplified and improved so that this book will also be a useful tool for research mathematicians. Information for our distributors: Titles in this series are copublished with the Clay Mathematics Institute (Cambridge, MA).
Book Synopsis Birational Geometry of Hypersurfaces by : Andreas Hochenegger
Download or read book Birational Geometry of Hypersurfaces written by Andreas Hochenegger and published by Springer Nature. This book was released on 2019-10-08 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originating from the School on Birational Geometry of Hypersurfaces, this volume focuses on the notion of (stable) rationality of projective varieties and, more specifically, hypersurfaces in projective spaces, and provides a large number of open questions, techniques and spectacular results. The aim of the school was to shed light on this vast area of research by concentrating on two main aspects: (1) Approaches focusing on (stable) rationality using deformation theory and Chow-theoretic tools like decomposition of the diagonal; (2) The connection between K3 surfaces, hyperkähler geometry and cubic fourfolds, which has both a Hodge-theoretic and a homological side. Featuring the beautiful lectures given at the school by Jean-Louis Colliot-Thélène, Daniel Huybrechts, Emanuele Macrì, and Claire Voisin, the volume also includes additional notes by János Kollár and an appendix by Andreas Hochenegger.
Book Synopsis The Geometry of Algebraic Cycles by : Reza Akhtar
Download or read book The Geometry of Algebraic Cycles written by Reza Akhtar and published by American Mathematical Soc.. This book was released on 2010 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of algebraic cycles has its roots in the study of divisors, extending as far back as the nineteenth century. Since then, and in particular in recent years, algebraic cycles have made a significant impact on many fields of mathematics, among them number theory, algebraic geometry, and mathematical physics. The present volume contains articles on all of the above aspects of algebraic cycles. It also contains a mixture of both research papers and expository articles, so that it would be of interest to both experts and beginners in the field.
Book Synopsis Persistence Theory: From Quiver Representations to Data Analysis by : Steve Y. Oudot
Download or read book Persistence Theory: From Quiver Representations to Data Analysis written by Steve Y. Oudot and published by American Mathematical Soc.. This book was released on 2017-05-17 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organized into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis.
Book Synopsis Spectral Decomposition and Eisenstein Series by : Colette Moeglin
Download or read book Spectral Decomposition and Eisenstein Series written by Colette Moeglin and published by Cambridge University Press. This book was released on 1995-11-02 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to automorphic forms, and Eisenstein series and pseudo-series, proving some of Langlands' work at the intersection of number theory and group theory.
Book Synopsis The Moduli Space of Curves by : Robert H. Dijkgraaf
Download or read book The Moduli Space of Curves written by Robert H. Dijkgraaf and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: The moduli space Mg of curves of fixed genus g – that is, the algebraic variety that parametrizes all curves of genus g – is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory.
Download or read book Moduli of Curves written by Joe Harris and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to a rich and fascinating subject: algebraic curves and how they vary in families. Providing a broad but compact overview of the field, this book is accessible to readers with a modest background in algebraic geometry. It develops many techniques, including Hilbert schemes, deformation theory, stable reduction, intersection theory, and geometric invariant theory, with the focus on examples and applications arising in the study of moduli of curves. From such foundations, the book goes on to show how moduli spaces of curves are constructed, illustrates typical applications with the proofs of the Brill-Noether and Gieseker-Petri theorems via limit linear series, and surveys the most important results about their geometry ranging from irreducibility and complete subvarieties to ample divisors and Kodaira dimension. With over 180 exercises and 70 figures, the book also provides a concise introduction to the main results and open problems about important topics which are not covered in detail.
Book Synopsis Lectures on Formal and Rigid Geometry by : Siegfried Bosch
Download or read book Lectures on Formal and Rigid Geometry written by Siegfried Bosch and published by Springer. This book was released on 2014-08-22 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster's Collaborative Research Center "Geometrical Structures in Mathematics".
Book Synopsis Algebraic Geometry by : Robin Hartshorne
Download or read book Algebraic Geometry written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
Download or read book Mirror Symmetry written by Kentaro Hori and published by American Mathematical Soc.. This book was released on 2003 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives with the aim of furthering interaction between the two fields. The material will be particularly useful for mathematicians and physicists who wish to advance their understanding across both disciplines. Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ``mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar-Vafa invariants. This book gives a single, cohesive treatment of mirror symmetry. Parts 1 and 2 develop the necessary mathematical and physical background from ``scratch''. The treatment is focused, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ``pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topi This one-of-a-kind book is suitable for graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics.
Book Synopsis Periods and Nori Motives by : Annette Huber
Download or read book Periods and Nori Motives written by Annette Huber and published by Springer. This book was released on 2017-03-08 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori’s abelian category of mixed motives. It develops Nori’s approach to mixed motives from scratch, thereby filling an important gap in the literature, and then explains the connection of mixed motives to periods, including a detailed account of the theory of period numbers in the sense of Kontsevich-Zagier and their structural properties. Period numbers are central to number theory and algebraic geometry, and also play an important role in other fields such as mathematical physics. There are long-standing conjectures about their transcendence properties, best understood in the language of cohomology of algebraic varieties or, more generally, motives. Readers of this book will discover that Nori’s unconditional construction of an abelian category of motives (over fields embeddable into the complex numbers) is particularly well suited for this purpose. Notably, Kontsevich's formal period algebra represents a torsor under the motivic Galois group in Nori's sense, and the period conjecture of Kontsevich and Zagier can be recast in this setting. Periods and Nori Motives is highly informative and will appeal to graduate students interested in algebraic geometry and number theory as well as researchers working in related fields. Containing relevant background material on topics such as singular cohomology, algebraic de Rham cohomology, diagram categories and rigid tensor categories, as well as many interesting examples, the overall presentation of this book is self-contained.
Download or read book The $K$-book written by Charles A. Weibel and published by American Mathematical Soc.. This book was released on 2013-06-13 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Informally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vector spaces and producing important intrinsic invariants which are useful in the study of algebr
