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Fourier-Mukai Transforms in Algebraic Geometry
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Fourier-Mukai Transforms in Algebraic Geometry

Daniel Huybrechts

Abstract

This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. Assuming a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. The derived category is a subtle invariant of the isomorphism type of a variety, and its group of autoequivalences often shows a rich structure. As it turns out — and this feature is pursued throughout the book — the behaviour of the derived category is determined by the geometric properties of the canonical bundle of ... More

Keywords: derived category, projective variety, coherent sheaf, abelian variety, K3 surface

Bibliographic Information

Print publication date: 2006 Print ISBN-13: 9780199296866
Published to Oxford Scholarship Online: September 2007 DOI:10.1093/acprof:oso/9780199296866.001.0001

Authors

Affiliations are at time of print publication.

Daniel Huybrechts, author
Mathematisches Institut, Universitaet Bonn

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