Semiorthogonal decompositions of derived categories of equivariant coherent sheaves

Details Semiorthogonal decompositions of derived categories of equivariant coherent sheaves Semiorthogonal decompositions of derived categories of equivariant coherent sheaves

2008-09-30

arxiv.org/abs/0809.5166v1

Izvestiya RAS: Mathematics, 73:5 (2009), 893-920; Izvestiya RAN, Ser. Mat., 73:5 (2009), 37--66 (in Russian)

Mathematics

Algebraic Geometry

28 pages, uses XY-pic

Scientific paper

Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of bounded derived category of G-equivariant coherent sheaves on X into components, equivalent to derived categories of twisted representations of the group. If the group is finite or reductive over the algebraically closed field of zero characteristic, this gives a full exceptional collection in the derived equivariant category. We apply our results to particular varieties such as projective spaces, quadrics, Grassmanians and Del Pezzo surfaces.

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