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Zusatztext It is a very good starting point to explore open problems related to derived categories, such as for example moduli space problems and birational classification. Informationen zum Autor Daniel Huybrechts completed his Ph.D. in 1992 at the Universität Berlin. He is now a professor at the Institut de Mathématiques de Jussieu, Université Paris VII. Klappentext This seminal text on Fourier-Mukai Transforms in Algebraic Geometry by a leading researcher and expositor is based on a course given at the Institut de Mathematiques de Jussieu in 2004 and 2005. Aimed at postgraduate students with a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. Including notions from other areas, e.g. singular cohomology, Hodge theory, abelian varieties, K3 surfaces; full proofs are given and exercises aid the reader throughout. Zusammenfassung This seminal text by a leading researcher is based on a course given at the Institut de Mathematiques de Jussieu. Aimed at students with a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. Full proofs are given and exercises aid the reader throughout. Inhaltsverzeichnis Preface 1: Triangulated categories 2: Derived categories: a quick tour 3: Derived categories of coherent sheaves 4: Derived category and canonical bundle I 5: Fourier-Mukai transforms 6: Derived category and canonical bundle II 7: Equivalence criteria for Fourier-Mukai transforms 8: Spherical and exceptional objects 9: Abelian varieties 10: K3 surfaces 11: Flips and flops 12: Derived categories of surfaces 13: Where to go from here References Index
