On The Arithmetic Of Toric Del Pezzo Surfaces

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Birational Geometry, Rational Curves, and Arithmetic

Author : Fedor Bogomolov
Publisher : Springer Science & Business Media
ISBN 13 : 146146482X
Total Pages : 324 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Birational Geometry, Rational Curves, and Arithmetic by : Fedor Bogomolov

Download or read book Birational Geometry, Rational Curves, and Arithmetic written by Fedor Bogomolov and published by Springer Science & Business Media. This book was released on 2013-05-17 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.

Strings, Gauge Fields, and the Geometry Behind

Author : Anton Rebhan
Publisher : World Scientific
ISBN 13 : 9814412546
Total Pages : 566 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Strings, Gauge Fields, and the Geometry Behind by : Anton Rebhan

Download or read book Strings, Gauge Fields, and the Geometry Behind written by Anton Rebhan and published by World Scientific. This book was released on 2013 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains exclusively invited contributions from collaborators of Maximilian Kreuzer, giving accounts of his scientific legacy and original articles from renowned theoretical physicists and mathematicians, including Victor Batyrev, Philip Candelas, Michael Douglas, Alexei Morozov, Joseph Polchinski, Peter van Nieuwenhuizen, and Peter West. Besides a collection of review and research articles from high-profile researchers in string theory and related fields of mathematics (in particular, algebraic geometry) which discuss recent progress in the exploration of string theory vacua and corresponding mathematical developments, this book contains a pedagogical account of the important work of Brandt, Dragon, and Kreuzer on classification of anomalies in gauge theories. This highly cited work, which is also quoted in the textbook of Steven Weinberg on quantum field theory, has not yet been presented in full detail except in private lecture notes by Norbert Dragon. Similarly, the software package PALP (Package for Analyzing Lattice Polytopes with applications to toric geometry), which has been incorporated in the SAGE (Software for Algebra and Geometry Experimentation) project, has not yet been documented in full detail. This book contains a user manual for a new thoroughly revised version of PALP. By including these two very useful original contributions, researchers in quantum field theory, string theory, and mathematics will find added value in a pedagogical presentation of the classification of quantum gauge field anomalies, and the accompanying comprehensive manual and tutorial for the powerful software package PALP.

Arithmetic Geometry

Author : Clay Mathematics Institute. Summer School
Publisher : American Mathematical Soc.
ISBN 13 : 0821844768
Total Pages : 570 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Arithmetic Geometry by : Clay Mathematics Institute. Summer School

Download or read book Arithmetic Geometry written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2009 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on survey lectures given at the 2006 Clay Summer School on Arithmetic Geometry at the Mathematics Institute of the University of Gottingen, this tile is intended for graduate students and recent PhD's. It introduces readers to modern techniques and conjectures at the interface of number theory and algebraic geometry.

Cox Rings

Author : Ivan Arzhantsev
Publisher : Cambridge University Press
ISBN 13 : 1107024625
Total Pages : 539 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Cox Rings by : Ivan Arzhantsev

Download or read book Cox Rings written by Ivan Arzhantsev and published by Cambridge University Press. This book was released on 2015 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a largely self-contained introduction to Cox rings and their applications in algebraic and arithmetic geometry.

Arithmetic of Higher-Dimensional Algebraic Varieties

Author : Bjorn Poonen
Publisher : Springer Science & Business Media
ISBN 13 : 0817681701
Total Pages : 292 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Arithmetic of Higher-Dimensional Algebraic Varieties by : Bjorn Poonen

Download or read book Arithmetic of Higher-Dimensional Algebraic Varieties written by Bjorn Poonen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text offers a collection of survey and research papers by leading specialists in the field documenting the current understanding of higher dimensional varieties. Recently, it has become clear that ideas from many branches of mathematics can be successfully employed in the study of rational and integral points. This book will be very valuable for researchers from these various fields who have an interest in arithmetic applications, specialists in arithmetic geometry itself, and graduate students wishing to pursue research in this area.

Arithmetic and Geometry Around Quantization

Author : Özgür Ceyhan
Publisher : Springer Science & Business Media
ISBN 13 : 0817648313
Total Pages : 295 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Arithmetic and Geometry Around Quantization by : Özgür Ceyhan

Download or read book Arithmetic and Geometry Around Quantization written by Özgür Ceyhan and published by Springer Science & Business Media. This book was released on 2010-01-12 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises both research and survey articles originating from the conference on Arithmetic and Geometry around Quantization held in Istanbul in 2006. A wide range of topics related to quantization are covered, thus aiming to give a glimpse of a broad subject in very different perspectives.

Quantitative Arithmetic of Projective Varieties

Author : Timothy D. Browning
Publisher : Springer Science & Business Media
ISBN 13 : 3034601298
Total Pages : 168 pages
Book Rating : 4.0/5 (346 download)

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Book Synopsis Quantitative Arithmetic of Projective Varieties by : Timothy D. Browning

Download or read book Quantitative Arithmetic of Projective Varieties written by Timothy D. Browning and published by Springer Science & Business Media. This book was released on 2009-12-21 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the range of available tools from analytic number theory that can be applied to study the density of rational points on projective varieties.

Calabi-Yau Varieties: Arithmetic, Geometry and Physics

Author : Radu Laza
Publisher : Springer
ISBN 13 : 1493928309
Total Pages : 542 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Calabi-Yau Varieties: Arithmetic, Geometry and Physics by : Radu Laza

Download or read book Calabi-Yau Varieties: Arithmetic, Geometry and Physics written by Radu Laza and published by Springer. This book was released on 2015-08-27 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area. The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.” The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.

Convex Bodies and Algebraic Geometry

Author : Tadao Oda
Publisher : Springer
ISBN 13 : 9783642725494
Total Pages : 0 pages
Book Rating : 4.7/5 (254 download)

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Book Synopsis Convex Bodies and Algebraic Geometry by : Tadao Oda

Download or read book Convex Bodies and Algebraic Geometry written by Tadao Oda and published by Springer. This book was released on 2012-02-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of toric varieties (also called torus embeddings) describes a fascinating interplay between algebraic geometry and the geometry of convex figures in real affine spaces. This book is a unified up-to-date survey of the various results and interesting applications found since toric varieties were introduced in the early 1970's. It is an updated and corrected English edition of the author's book in Japanese published by Kinokuniya, Tokyo in 1985. Toric varieties are here treated as complex analytic spaces. Without assuming much prior knowledge of algebraic geometry, the author shows how elementary convex figures give rise to interesting complex analytic spaces. Easily visualized convex geometry is then used to describe algebraic geometry for these spaces, such as line bundles, projectivity, automorphism groups, birational transformations, differential forms and Mori's theory. Hence this book might serve as an accessible introduction to current algebraic geometry. Conversely, the algebraic geometry of toric varieties gives new insight into continued fractions as well as their higher-dimensional analogues, the isoperimetric problem and other questions on convex bodies. Relevant results on convex geometry are collected together in the appendix.

Monomial Resolutions and the Cox Rings of Del Pezzo Surfaces

Author : Mauricio Fernando Velasco
Publisher :
ISBN 13 :
Total Pages : 240 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Monomial Resolutions and the Cox Rings of Del Pezzo Surfaces by : Mauricio Fernando Velasco

Download or read book Monomial Resolutions and the Cox Rings of Del Pezzo Surfaces written by Mauricio Fernando Velasco and published by . This book was released on 2007 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Arithmetic and Geometry

Author : Luis Dieulefait
Publisher : Cambridge University Press
ISBN 13 : 1316381447
Total Pages : 539 pages
Book Rating : 4.3/5 (163 download)

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Book Synopsis Arithmetic and Geometry by : Luis Dieulefait

Download or read book Arithmetic and Geometry written by Luis Dieulefait and published by Cambridge University Press. This book was released on 2015-10-08 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 'Arithmetic and Geometry' trimester, held at the Hausdorff Research Institute for Mathematics in Bonn, focussed on recent work on Serre's conjecture and on rational points on algebraic varieties. The resulting proceedings volume provides a modern overview of the subject for graduate students in arithmetic geometry and Diophantine geometry. It is also essential reading for any researcher wishing to keep abreast of the latest developments in the field. Highlights include Tim Browning's survey on applications of the circle method to rational points on algebraic varieties and Per Salberger's chapter on rational points on cubic hypersurfaces.

Arithmetic, Geometry, Cryptography and Coding Theory

Author : Stéphane Ballet
Publisher : American Mathematical Soc.
ISBN 13 : 1470454262
Total Pages : 303 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Arithmetic, Geometry, Cryptography and Coding Theory by : Stéphane Ballet

Download or read book Arithmetic, Geometry, Cryptography and Coding Theory written by Stéphane Ballet and published by American Mathematical Soc.. This book was released on 2021-07-01 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 17th International Conference on Arithmetic, Geometry, Cryptography and Coding Theory (AGC2T-17), held from June 10–14, 2019, at the Centre International de Rencontres Mathématiques in Marseille, France. The conference was dedicated to the memory of Gilles Lachaud, one of the founding fathers of the AGC2T series. Since the first meeting in 1987 the biennial AGC2T meetings have brought together the leading experts on arithmetic and algebraic geometry, and the connections to coding theory, cryptography, and algorithmic complexity. This volume highlights important new developments in the field.

Computational Methods for Algebraic Spline Surfaces

Author : Tor Dokken
Publisher : Springer Science & Business Media
ISBN 13 : 3540271570
Total Pages : 239 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Computational Methods for Algebraic Spline Surfaces by : Tor Dokken

Download or read book Computational Methods for Algebraic Spline Surfaces written by Tor Dokken and published by Springer Science & Business Media. This book was released on 2006-05-24 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains revised papers that were presented at the international workshop entitled Computational Methods for Algebraic Spline Surfaces (“COMPASS”), which was held from September 29 to October 3, 2003, at Schloß Weinberg, Kefermarkt (A- tria). The workshop was mainly devoted to approximate algebraic geometry and its - plications. The organizers wanted to emphasize the novel idea of approximate implici- zation, that has strengthened the existing link between CAD / CAGD (Computer Aided Geometric Design) and classical algebraic geometry. The existing methods for exact implicitization (i. e. , for conversion from the parametric to an implicit representation of a curve or surface) require exact arithmetic and are too slow and too expensive for industrial use. Thus the duality of an implicit representation and a parametric repres- tation is only used for low degree algebraic surfaces such as planes, spheres, cylinders, cones and toroidal surfaces. On the other hand, this duality is a very useful tool for - veloping ef?cient algorithms. Approximate implicitization makes this duality available for general curves and surfaces. The traditional exact implicitization of parametric surfaces produce global rep- sentations, which are exact everywhere. The surface patches used in CAD, however, are always de?ned within a small box only; they are obtained for a bounded parameter domain (typically a rectangle, or – in the case of “trimmed” surface patches – a subset of a rectangle). Consequently, a globally exact representation is not really needed in practice.

Arithmetic Geometry

Author : Jean-Louis Colliot-Thélène
Publisher : Springer
ISBN 13 : 3642159451
Total Pages : 251 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Arithmetic Geometry by : Jean-Louis Colliot-Thélène

Download or read book Arithmetic Geometry written by Jean-Louis Colliot-Thélène and published by Springer. This book was released on 2010-10-27 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties through arbitrary rings, in particular through non-algebraically closed fields. It lies at the intersection between classical algebraic geometry and number theory. A C.I.M.E. Summer School devoted to arithmetic geometry was held in Cetraro, Italy in September 2007, and presented some of the most interesting new developments in arithmetic geometry. This book collects the lecture notes which were written up by the speakers. The main topics concern diophantine equations, local-global principles, diophantine approximation and its relations to Nevanlinna theory, and rationally connected varieties. The book is divided into three parts, corresponding to the courses given by J-L Colliot-Thelene, Peter Swinnerton Dyer and Paul Vojta.

Rational Points on Algebraic Varieties

Author : Emmanuel Peyre
Publisher : Birkhäuser
ISBN 13 : 3034883684
Total Pages : 455 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Rational Points on Algebraic Varieties by : Emmanuel Peyre

Download or read book Rational Points on Algebraic Varieties written by Emmanuel Peyre and published by Birkhäuser. This book was released on 2012-12-06 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of rational and integral points on higher-dimensional algebraic varieties. It contains carefully selected research papers addressing the arithmetic geometry of varieties which are not of general type, with an emphasis on how rational points are distributed with respect to the classical, Zariski and adelic topologies. The present volume gives a glimpse of the state of the art of this rapidly expanding domain in arithmetic geometry. The techniques involve explicit geometric constructions, ideas from the minimal model program in algebraic geometry as well as analytic number theory and harmonic analysis on adelic groups.

Analytic Number Theory

Author : William Duke
Publisher : American Mathematical Soc.
ISBN 13 : 9780821843079
Total Pages : 270 pages
Book Rating : 4.8/5 (43 download)

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Book Synopsis Analytic Number Theory by : William Duke

Download or read book Analytic Number Theory written by William Duke and published by American Mathematical Soc.. This book was released on 2007 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles in this volume are based on talks given at the Gauss-Dirichlet Conference held in Gottingen on June 20-24, 2005. The conference commemorated the 150th anniversary of the death of C.-F. Gauss and the 200th anniversary of the birth of J.-L. Dirichlet. The volume begins with a definitive summary of the life and work of Dirichlet and continues with thirteen papers by leading experts on research topics of current interest in number theory that were directly influenced by Gauss and Dirichlet. Among the topics are the distribution of primes (long arithmetic progressions of primes and small gaps between primes), class groups of binary quadratic forms, various aspects of the theory of $L$-functions, the theory of modular forms, and the study of rational and integral solutions to polynomial equations in several variables. Information for our distributors: Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

Geometry Over Nonclosed Fields

Author : Fedor Bogomolov
Publisher : Springer
ISBN 13 : 3319497634
Total Pages : 267 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Geometry Over Nonclosed Fields by : Fedor Bogomolov

Download or read book Geometry Over Nonclosed Fields written by Fedor Bogomolov and published by Springer. This book was released on 2017-02-09 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems. There has been significant progress in this field with major new results, which have given new impetus to the study of rational curves and spaces of rational curves on K3 surfaces and their higher-dimensional generalizations. One main recent insight the book covers is the idea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces. The implementation of this idea led to proofs of long-standing conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new theorems in arithmetic. This proceedings volume covers these new insights in detail.