Derived categories of coherent sheaves

Details Derived categories of coherent sheaves Derived categories of coherent sheaves

2006-02-07

arxiv.org/abs/math/0602129v1

Mathematics

Algebraic Geometry

Survey article for ICM 2006. Preliminary version; corrections and comments welcome

Scientific paper

We discuss derived categories of coherent sheaves on algebraic varieties. We focus on the case of non-singular Calabi-Yau varieties and consider two unsolved problems: proving that birational varieties have equivalent derived categories, and computing the group of derived autoequivalences. We also introduce the space of stability conditions on a triangulated category and explain its relevance to these two problems.

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