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Title: Fourier-Mukai transforms in algebraic geometry ([Ebook]) / D. Huybrechts. Dewey Class: 516.35 (DDC 22) Author: Huybrechts, Daniel. Publication: Oxford : Oxford University Press, 2007 Other name(s): Oxford Scholarship Online Physical Details: 1 online resource Series: Oxford mathematical monographs ISBN: 9780191711329 Note: Print publication date: 2006. - Published to Oxford Scholarship Online: September 2007 Mode of acces to digital resource: Electronic reproduction.Oxford :Oxford University Press,2007. -Oxford Scholarship OnlineMode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher) System details note: Online access to this digital book is restricted to subscribing institutions through IP address (only for SISSA internal users) Summary Note: 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.: ------------------------------ *** There are no holdings for this record *** -----------------------------------------------
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