Derived categories and Kummer varieties

Details Derived categories and Kummer varieties Derived categories and Kummer varieties

2006-02-18

arxiv.org/abs/math/0602399v2

Mathematics

Algebraic Geometry

14 pages. Minor changes (theorem numbering slightly changed). Final version to appear in Math. Zeit

Scientific paper

We prove that if two abelian varieties have equivalent derived categories then the derived categories of the smooth stacks associated to the corresponding Kummer varieties are equivalent as well. The second main result establishes necessary and sufficient conditions for the existence of equivalences between the twisted derived categories of two Kummer surfaces in terms of Hodge isometries between the generalized transcendental lattices of the corresponding abelian surfaces.

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