Fano varieties of cubic fourfolds containing a plane

Abstract

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.

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

References in corpus (3)

• A global Torelli theorem for hyperkahler manifolds
• Transcendental obstructions to weak approximation on general K3 surfaces
• Bridgeland-Stable Moduli Spaces for K-Trivial Surfaces

Cited by in corpus (1)

• Transcendental obstructions to weak approximation on general K3 surfaces