Fano varieties of cubic fourfolds containing a plane

By Emanuele Macrì, P. Stellari. 2009

54 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b33cde9b97e023e06a534776ee5861d476ec7307

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Hodge theory and derived categories of cubic fourfolds (2012, unknown): “His conjecture has attracted a great deal of interest recently [33, 7, 5].”
Stability conditions on Kuznetsov components (2017, methodology): “forward from previous descriptions of Ku(X) for gX ∈ {10,12}, due to [BMMS12] for gX = 8, and new for gX = 6. For cubic fourfolds containing a plane, stability conditions on Ku(X) were constructed in [MS12], and Gepner point stability conditions2 were obtained in [Tod16]. In this case, Ku(X) is equi”
Transcendental obstructions to weak approximation on general K3 surfaces (2010, background): “ α∈ Br(X)[2]; van Geemen [vG05, §9] oﬀers geometric interpretations for the classes we have not considered. (4) Macri and Stellari have recast this discussion in the language of α-twisted sheaves on X[MS09]. 3. Quadratic forms and maximal isotropicsubspaces To generalize the constructions of §2, we ”