Fourier-Mukai Transforms in Algebraic Geometry [Hardcover]

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.

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