Derived categories of sheaves: a skimming

Details Derived categories of sheaves: a skimming Derived categories of sheaves: a skimming

2005-01-06

arxiv.org/abs/math/0501094v1

Mathematics

Algebraic Geometry

Lecture notes from Snowbird and Lukecin

Scientific paper

These lecture notes were prepared for the workshop ``Algebraic Geometry: Presentations by Young Researchers'' in Snowbird, Utah, July 2004, and for the autumn school in Lukecin, Poland, September 2004. In six lectures I attempted to present a non-technical introduction to derived categories of sheaves on varieties, including some important results like: -- the description of the derived category of P^n; -- Serre duality; -- the Bondal-Orlov result about derived categories of varieties with ample or antiample canonical class; -- the Mukai-Bondal-Orlov-Bridgeland criterion for equivalence; -- equivalences for K3 surfaces and abelian varieties; -- invariance of Hochschild homology and cohomology under derived equivalence.

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