Cohomology Of Coherent Sheaves On Projective Varieties

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Cohomology Of Coherent Sheaves On Projective Varieties

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Author : Rahul Pandharipande
language : en
Publisher:
Release Date : 1990

Cohomology Of Coherent Sheaves On Projective Varieties written by Rahul Pandharipande and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.

Residues And Duality For Projective Algebraic Varieties

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Author : Ernst Kunz
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Residues And Duality For Projective Algebraic Varieties written by Ernst Kunz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

"This book, which grew out of lectures by E. Kunz for students with a background in algebra and algebraic geometry, develops local and global duality theory in the special case of (possibly singular) algebraic varieties over algebraically closed base fields. It describes duality and residue theorems in terms of Kahler differential forms and their residues. The properties of residues are introduced via local cohomology. Special emphasis is given to the relation between residues to classical results of algebraic geometry and their generalizations." "The contribution by A. Dickenstein gives applications of residues and duality to polynomial solutions of constant coefficient partial differential equations and to problems in interpolation and ideal membership, D. A. Cox explains toric residues and relates them to the earlier text." "The book is intended as an introduction to more advanced treatments and further applications of the subject, to which numerous bibliographical hints are given."--BOOK JACKET.

Topics In Cohomological Studies Of Algebraic Varieties

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Author : Piotr Pragacz
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30

Topics In Cohomological Studies Of Algebraic Varieties written by Piotr Pragacz 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 2006-03-30 with Mathematics categories.

The articles in this volume study various cohomological aspects of algebraic varieties: - characteristic classes of singular varieties; - geometry of flag varieties; - cohomological computations for homogeneous spaces; - K-theory of algebraic varieties; - quantum cohomology and Gromov-Witten theory. The main purpose is to give comprehensive introductions to the above topics through a series of "friendly" texts starting from a very elementary level and ending with the discussion of current research. In the articles, the reader will find classical results and methods as well as new ones. Numerous examples will help to understand the mysteries of the cohomological theories presented. The book will be a useful guide to research in the above-mentioned areas. It is adressed to researchers and graduate students in algebraic geometry, algebraic topology, and singularity theory, as well as to mathematicians interested in homogeneous varieties and symmetric functions. Most of the material exposed in the volume has not appeared in books before. Contributors: Paolo Aluffi Michel Brion Anders Skovsted Buch Haibao Duan Ali Ulas Ozgur Kisisel Piotr Pragacz Jörg Schürmann Marek Szyjewski Harry Tamvakis

Algebraic Geometry 2

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Author : Kenji Ueno
language : en
Publisher: American Mathematical Soc.
Release Date : 1999

Algebraic Geometry 2 written by Kenji Ueno and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

Algebraic geometry is built upon two fundamental notions: schemes and sheaves. The theory of schemes was explained in Algebraic Geometry 1: From Algebraic Varieties to Schemes. In this volume, the author turns to the theory of sheaves and their cohomology. A sheaf is a way of keeping track of local information defined on a topological space, such as the local holomorphic functions on a complex manifold or the local sections of a vector bundle. To study schemes, it is useful to study the sheaves defined on them, especially the coherent and quasicoherent sheaves.

Lectures On Algebraic Geometry Ii

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Author : Günter Harder
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-21

Lectures On Algebraic Geometry Ii written by Günter Harder 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 2011-04-21 with Mathematics categories.

This second volume introduces the concept of shemes, reviews some commutative algebra and introduces projective schemes. The finiteness theorem for coherent sheaves is proved, here again the techniques of homological algebra and sheaf cohomology are needed. In the last two chapters, projective curves over an arbitrary ground field are discussed, the theory of Jacobians is developed, and the existence of the Picard scheme is proved. Finally, the author gives some outlook into further developments- for instance étale cohomology- and states some fundamental theorems.

Algebraic Geometry Ii

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Author : I.R. Shafarevich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-22

Algebraic Geometry Ii written by I.R. Shafarevich 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 2013-11-22 with Mathematics categories.

This two-part volume contains numerous examples and insights on various topics. The authors have taken pains to present the material rigorously and coherently. This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields.

On The De Rham Cohomology Of Algebraic Varieties

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Author : Robin Hartshorne
language : en
Publisher:
Release Date : 1975

On The De Rham Cohomology Of Algebraic Varieties written by Robin Hartshorne and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.

Ample Subvarieties Of Algebraic Varieties

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Author : Robin Hartshorne
language : en
Publisher: Springer
Release Date : 2006-11-15

Ample Subvarieties Of Algebraic Varieties written by Robin Hartshorne and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Vector Bundles On Complex Projective Spaces

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Author : Christian Okonek
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-24

Vector Bundles On Complex Projective Spaces written by Christian Okonek 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 2011-06-24 with Mathematics categories.

These lecture notes are intended as an introduction to the methods of classi?cation of holomorphic vector bundles over projective algebraic manifolds X. To be as concrete as possible we have mostly restricted ourselves to the case X = P . According to Serre (GAGA) the class- n cation of holomorphic vector bundles is equivalent to the classi?cation of algebraic vector bundles. Here we have used almost exclusively the language of analytic geometry. The book is intended for students who have a basic knowledge of analytic and (or) algebraic geometry. Some fundamental results from these ?elds are summarized at the beginning. One of the authors gave a survey in the S ́eminaire Bourbaki 1978 on the current state of the classi?cation of holomorphic vector bundles over P . This lecture then served as the basis for a course of lectures n in G ̈ottingen in the Winter Semester 78/79. The present work is an extended and up-dated exposition of that course. Because of the - troductory nature of this book we have had to leave out some di?cult topics such as the restriction theorem of Barth. As compensation we have appended to each section a paragraph in which historical remarks are made, further results indicated and unsolved problems presented. The book is divided into two chapters. Each chapter is subdivided into several sections which in turn are made up of a number of pa- graphs. Each section is preceded by a short description of its contents.

The Geometry Of Moduli Spaces Of Sheaves

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Author : Daniel Huybrechts
language : en
Publisher: Cambridge University Press
Release Date : 2010-05-27

The Geometry Of Moduli Spaces Of Sheaves 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 2010-05-27 with Mathematics categories.

This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.