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.
Fano varieties of cubic fourfolds containing a plane / E. Macrì, P. Stellari. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 354:3(2012), pp. 1147-1176. [10.1007/s00208-011-0776-7]
Fano varieties of cubic fourfolds containing a plane
P. StellariUltimo
2012
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.File in questo prodotto:
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