Author : Daniel Huybrechts
Publisher : Oxford University Press
Page : 316 pages
File Size : 38,53 MB
Release : 2006-04-20
Category : Mathematics
ISBN : 0199296863
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.
Author : CLAUDIO BARTOCCI
Publisher : Springer Science & Business Media
Page : 435 pages
File Size : 36,86 MB
Release : 2009-06-12
Category : Science
ISBN : 0817646639
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.
Author : Alexander Polishchuk
Publisher : Cambridge University Press
Page : 308 pages
File Size : 44,57 MB
Release : 2003-04-21
Category : Mathematics
ISBN : 0521808049
Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.
Author : Daniel Huybrechts
Publisher :
Page : 307 pages
File Size : 34,44 MB
Release : 2006
Category : Electronic books
ISBN :
Author : Spencer Bloch
Publisher : Cambridge University Press
Page : 155 pages
File Size : 24,21 MB
Release : 2010-07-22
Category : Mathematics
ISBN : 1139487825
Spencer Bloch's 1979 Duke lectures, a milestone in modern mathematics, have been out of print almost since their first publication in 1980, yet they have remained influential and are still the best place to learn the guiding philosophy of algebraic cycles and motives. This edition, now professionally typeset, has a new preface by the author giving his perspective on developments in the field over the past 30 years. The theory of algebraic cycles encompasses such central problems in mathematics as the Hodge conjecture and the Bloch–Kato conjecture on special values of zeta functions. The book begins with Mumford's example showing that the Chow group of zero-cycles on an algebraic variety can be infinite-dimensional, and explains how Hodge theory and algebraic K-theory give new insights into this and other phenomena.
Author : Jingyi Chen
Publisher : Springer Nature
Page : 615 pages
File Size : 45,89 MB
Release : 2020-04-10
Category : Mathematics
ISBN : 3030349535
This edited volume has a two-fold purpose. First, comprehensive survey articles provide a way for beginners to ease into the corresponding sub-fields. These are then supplemented by original works that give the more advanced readers a glimpse of the current research in geometric analysis and related PDEs. The book is of significant interest for researchers, including advanced Ph.D. students, working in geometric analysis. Readers who have a secondary interest in geometric analysis will benefit from the survey articles. The results included in this book will stimulate further advances in the subjects: geometric analysis, including complex differential geometry, symplectic geometry, PDEs with a geometric origin, and geometry related to topology. Contributions by Claudio Arezzo, Alberto Della Vedova, Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis, Sun-Yung A. Chang, Zheng-Chao Han, Paul Yang, Tobias Holck Colding, William P. Minicozzi II, Panagiotis Dimakis, Richard Melrose, Akito Futaki, Hajime Ono, Jiyuan Han, Jeff A. Viaclovsky, Bruce Kleiner, John Lott, Sławomir Kołodziej, Ngoc Cuong Nguyen, Chi Li, Yuchen Liu, Chenyang Xu, YanYan Li, Luc Nguyen, Bo Wang, Shiguang Ma, Jie Qing, Xiaonan Ma, Sean Timothy Paul, Kyriakos Sergiou, Tristan Rivière, Yanir A. Rubinstein, Natasa Sesum, Jian Song, Jeffrey Streets, Neil S. Trudinger, Yu Yuan, Weiping Zhang, Xiaohua Zhu and Aleksey Zinger.
Author : Daniel Huybrechts
Publisher : Cambridge University Press
Page : 345 pages
File Size : 36,38 MB
Release : 2010-05-27
Category : Mathematics
ISBN : 1139485822
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.
Author : Daniel Huybrechts
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 25,42 MB
Release : 2005
Category : Computers
ISBN : 9783540212904
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)
Author : Arnaud Beauville
Publisher : Cambridge University Press
Page : 148 pages
File Size : 32,8 MB
Release : 1996-06-28
Category : Mathematics
ISBN : 9780521498425
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.
Author : Hiraku Nakajima
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 25,84 MB
Release : 1999
Category : Mathematics
ISBN : 0821819569
It has been realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory - even theoretical physics. This book reflects this feature of Hilbert schemes.
