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• W587747628 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." @default.
• W587747628 created "2016-06-24" @default.
• W587747628 creator A5010170221 @default.
• W587747628 date "2006-04-20" @default.
• W587747628 modified "2023-10-12" @default.
• W587747628 title "Fourier-Mukai Transforms in Algebraic Geometry" @default.
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• W587747628 doi "https://doi.org/10.1093/acprof:oso/9780199296866.001.0001" @default.
• W587747628 hasPublicationYear "2006" @default.
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