Fourier Mukai Transforms In Algebraic Geometry

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Fourier Mukai Transforms In Algebraic Geometry

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Author : Daniel Huybrechts
language : en
Publisher: Clarendon Press
Release Date : 2006-04-20

Fourier Mukai Transforms In Algebraic Geometry written by Daniel Huybrechts and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-20 with Mathematics categories.

This seminal text on Fourier-Mukai Transforms in Algebraic Geometry by a leading researcher and expositor is based on a course given at the Institut de Mathematiques de Jussieu in 2004 and 2005. Aimed at postgraduate students with a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. Including notions from other areas, e.g. singular cohomology, Hodge theory, abelian varieties, K3 surfaces; full proofs are given and exercises aid the reader throughout.

Fourier Mukai And Nahm Transforms In Geometry And Mathematical Physics

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Author : CLAUDIO BARTOCCI
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-12

Fourier Mukai And Nahm Transforms In Geometry And Mathematical Physics written by CLAUDIO BARTOCCI and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-12 with Science categories.

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.

Abelian Varieties Theta Functions And The Fourier Transform

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Author : Alexander Polishchuk
language : en
Publisher: Cambridge University Press
Release Date : 2003-04-21

Abelian Varieties Theta Functions And The Fourier Transform written by Alexander Polishchuk and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-21 with Mathematics categories.

Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.

Algebraic And Geometric Surgery

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Author : Andrew Ranicki
language : en
Publisher: Oxford University Press
Release Date : 2002

Algebraic And Geometric Surgery written by Andrew Ranicki and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

This book is an introduction to surgery theory: the standard classification method for high-dimensional manifolds. It is aimed at graduate students who have already had a basic topology course, and would now like to understand the topology of high-dimensional manifolds. This text contains entry-level accounts of the various prerequisites of both algebra and topology, including basic homotopy and homology, Poincare duality, bundles, cobordism, embeddings, immersions, Whitehead torsion, Poincare complexes, spherical fibrations and quadratic forms and formations. While concentrating on the basic mechanics of surgery, this book includes many worked examples, useful drawings for illustration of the algebra and references for further reading.

Complex Geometry

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Author : Daniel Huybrechts
language : en
Publisher: Springer Science & Business Media
Release Date : 2005

Complex Geometry written by Daniel Huybrechts and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Computers categories.

Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

Complex Algebraic Surfaces

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Author : Arnaud Beauville
language : en
Publisher: Cambridge University Press
Release Date : 1996-06-28

Complex Algebraic Surfaces written by Arnaud Beauville and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-06-28 with Mathematics categories.

Developed over more than a century, and still an active area of research today, the classification of algebraic surfaces is an intricate and fascinating branch of mathematics. In this book Professor BeauviIle gives a lucid and concise account of the subject, following the strategy of F. Enriques, but expressed simply in the language of modern topology and sheaf theory, so as to be accessible to any budding geometer. This volume is self contained and the exercises succeed both in giving the flavour of the extraordinary wealth of examples in the classical subject, and in equipping the reader with most of the techniques needed for research.

Methods Of Homological Algebra

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Author : Sergei I. Gelfand
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Methods Of Homological Algebra written by Sergei I. Gelfand and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics, and its contemporary applications are many and diverse. This modern approach to homological algebra, by two leading writers in the field, is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory (sheaf cohomology, spectral sequences, etc.) are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn a modern approach to homological algebra and to use it in their work. For the second edition the authors have made numerous corrections.

Lectures On K3 Surfaces

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Author : Daniel Huybrechts
language : en
Publisher: Cambridge University Press
Release Date : 2016-09-26

Lectures On K3 Surfaces written by Daniel Huybrechts and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-26 with Mathematics categories.

Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.

Algebraic Geometry

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Author : Robin Hartshorne
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Algebraic Geometry written by Robin Hartshorne and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. After receiving his Ph.D. from Princeton in 1963, Hartshorne became a Junior Fellow at Harvard, then taught there for several years. In 1972 he moved to California where he is now Professor at the University of California at Berkeley. He is the author of "Residues and Duality" (1966), "Foundations of Projective Geometry (1968), "Ample Subvarieties of Algebraic Varieties" (1970), and numerous research titles. His current research interest is the geometry of projective varieties and vector bundles. He has been a visiting professor at the College de France and at Kyoto University, where he gave lectures in French and in Japanese, respectively. Professor Hartshorne is married to Edie Churchill, educator and psychotherapist, and has two sons. He has travelled widely, speaks several foreign languages, and is an experienced mountain climber. He is also an accomplished amateur musician: he has played the flute for many years, and during his last visit to Kyoto he began studying the shakuhachi.