Fourier-Mukai Transforms in Algebraic Geometry Oxford Mathematical Monographs Series

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.

Triangulated categories. Derived categories: a quick tour. Derived categories of coherent sheaves. Derived category and canonical bundle I. Fourier-Mukai transforms. Derived category and canonical bundle II. Equivalence criteria for Fourier-Mukai transforms. Spherical and exceptional objects. Abelian varieties. K3 surfaces. Flips and flops. Derived categories of surfaces. Where to go from here.

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.