Fourier-Mukai Transforms in Algebraic Geometry

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ID: 305592
2006
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Abstract
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 the variety. Including notions from other areas, e.g., singular cohomology, Hodge theory, abelian varieties, K3 surfaces; full proofs and exercises are provided. The final chapter summarizes recent research directions, such as connections to orbifolds and the representation theory of finite groups via the McKay correspondence, stability conditions on triangulated categories, and the notion of the derived category of sheaves twisted by a gerbe.
Reference Key
openalex_W587747628 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Daniel Huybrechts
Journal Oxford University Press eBooks
Year 2006
DOI
10.1093/acprof:oso/9780199296866.001.0001
URL
https://doi.org/10.1093/acprof:oso/9780199296866.001.0001
Keywords Keywords not found

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