Fourier-Mukai Transforms in Algebraic Geometry

Fourier-Mukai Transforms in Algebraic Geometry

Author: Daniel Huybrechts

Publisher: Oxford University Press on Demand

ISBN: 9780199296866

Category: Mathematics

Page: 316

View: 193

This work is based on a course given at the Institut de Mathematiques de Jussieu, on the derived category of coherent sheaves on a smooth projective variety. It is aimed at students with a basic knowledge of algebraic geometry and contains full proofs and exercises that aid the reader.

Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics

Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics

Author: CLAUDIO BARTOCCI

Publisher: Springer Science & Business Media

ISBN: 9780817646639

Category: Science

Page: 418

View: 158

Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries. In the last three decades the development of a number of novel ideas in algebraic geometry, category theory, gauge theory, and string theory has been closely related to generalizations of integral transforms of a more geometric character. "Fourier–Mukai and Nahm Transforms in Geometry and Mathematical Physics" examines the algebro-geometric approach (Fourier–Mukai functors) as well as the differential-geometric constructions (Nahm). Also included is a considerable amount of material from existing literature which has not been systematically organized into a monograph. Key features: Basic constructions and definitions are presented in preliminary background chapters - Presentation explores applications and suggests several open questions - Extensive bibliography and index. This self-contained monograph provides an introduction to current research in geometry and mathematical physics and is intended for graduate students and researchers just entering this field.

A Celebration of Algebraic Geometry

A Celebration of Algebraic Geometry

Author: Brendan Hassett

Publisher: American Mathematical Soc.

ISBN: 9780821889831

Category: Mathematics

Page: 599

View: 677

This volume resulted from the conference A Celebration of Algebraic Geometry, which was held at Harvard University from August 25-28, 2011, in honor of Joe Harris' 60th birthday. Harris is famous around the world for his lively textbooks and enthusiastic teaching, as well as for his seminal research contributions. The articles are written in this spirit: clear, original, engaging, enlivened by examples, and accessible to young mathematicians. The articles in this volume focus on the moduli space of curves and more general varieties, commutative algebra, invariant theory, enumerative geometry both classical and modern, rationally connected and Fano varieties, Hodge theory and abelian varieties, and Calabi-Yau and hyperkähler manifolds. Taken together, they present a comprehensive view of the long frontier of current knowledge in algebraic geometry. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

Algebraic Geometry, Seattle 2005

Algebraic Geometry, Seattle 2005

Author: Dan Abramovich

Publisher: American Mathematical Soc.

ISBN: 9780821847022

Category: Mathematics

Page: 1004

View: 410

This volume contains research and expository papers by some of the speakers at the 2005 AMS Summer Institute on Algebraic Geometry. Numerous papers delve into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties.

Recent Advances in Algebraic Geometry

Recent Advances in Algebraic Geometry

Author: Christopher D. Hacon

Publisher: Cambridge University Press

ISBN: 9781316195833

Category: Mathematics

Page:

View: 471

Contemporary research in algebraic geometry is the focus of this collection, which presents articles on modern aspects of the subject. The list of topics covered is a roll-call of some of the most important and active themes in this thriving area of mathematics: the reader will find articles on birational geometry, vanishing theorems, complex geometry and Hodge theory, free resolutions and syzygies, derived categories, invariant theory, moduli spaces, and related topics, all written by leading experts. The articles, which have an expository flavour, present an overall picture of current research in algebraic geometry, making this book essential for researchers and graduate students. This volume is the outcome of the conference Recent Advances in Algebraic Geometry, held in Ann Arbor, Michigan, to honour Rob Lazarsfeld's many contributions to the subject on the occasion of his 60th birthday.

Algebraic Geometry: Salt Lake City 2015 (Part 1)

Algebraic Geometry: Salt Lake City 2015 (Part 1)

Author: Tommaso de Fernex

Publisher: American Mathematical Soc.

ISBN: 9781470435776

Category: Geometry, Algebraic

Page: 655

View: 458

This is Part 1 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic and -adic tools, etc. The resulting articles will be important references in these areas for years to come.

Surveys on Recent Developments in Algebraic Geometry

Surveys on Recent Developments in Algebraic Geometry

Author: Izzet Coskun

Publisher: American Mathematical Soc.

ISBN: 9781470435578

Category: $K$-theory -- Higher algebraic $K$-theory -- $Q$- and plus-constructions

Page: 370

View: 102

The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah. These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.

Geometry Over Nonclosed Fields

Geometry Over Nonclosed Fields

Author: Fedor Bogomolov

Publisher: Springer

ISBN: 9783319497631

Category: Mathematics

Page: 261

View: 450

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.

New Trends in Algebraic Geometry

New Trends in Algebraic Geometry

Author: England) Euroconference on Algebraic Geometry (1996 Warwick

Publisher: Cambridge University Press

ISBN: 0521646596

Category: Mathematics

Page: 484

View: 121

This book is the outcome of the 1996 Warwick Algebraic Geometry EuroConference, containing seventeen survey and research articles selected from the most outstanding contemporary research topics in algebraic geometry. Several of the articles are expository: among these a beautiful short exposition by Paranjape of the new and very simple approach to the resolution of singularities; a detailed essay by Ito and Nakamura on the ubiquitous A,D,E classification, centered around simple surface singularities; a discussion by Morrison of the new special Lagrangian approach to giving geometric foundations to mirror symmetry; and two deep, informative surveys by Siebert and Behrend on Gromow-Witten invariants, treating them from the point of view of algebraic and symplectic geometry. The remaining articles cover a wide cross section of the most significant research topics in algebraic geometry. This includes Gromow-Witten invariants, Hodge theory, Calabi-Yau 3-folds, mirror symmetry and classification of varieties.

Ulrich Bundles

Ulrich Bundles

Author: Laura Costa

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783110647686

Category: Mathematics

Page: 282

View: 135

The goal of this book is to cover the active developments of arithmetically Cohen-Macaulay and Ulrich bundles and related topics in the last 30 years, and to present relevant techniques and multiple applications of the theory of Ulrich bundles to a wide range of problems in algebraic geometry as well as in commutative algebra.