Fano varieties of cubic fourfolds containing a plane

Details Fano varieties of cubic fourfolds containing a plane Fano varieties of cubic fourfolds containing a plane

2009-09-15

arxiv.org/abs/0909.2725v2

Mathematics

Algebraic Geometry

26 pages. Many changes in the exposition. Final version to appear in Math. Ann

Scientific paper

We prove that the Fano variety of lines of a generic cubic fourfold containing a plane is isomorphic to a moduli space of twisted stable complexes on a K3 surface. On the other hand, we show that the Fano varieties are always birational to moduli spaces of twisted stable coherent sheaves on a K3 surface. The moduli spaces of complexes and of sheaves are related by wall-crossing in the derived category of twisted sheaves on the corresponding K3 surface.

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