| Résume | Abstract: Given a plane contained in a cubic fourfold, one can construct an associated K3 surface equipped with a Brauer class, such that the twisted derived category of the K3 surface is equivalent to the Kuznetsov component of the cubic fourfold.
In this talk, we consider the case where the cubic fourfold contains (at least) two planes. There are three 18-dimensional families of such cubic fourfolds, depending on how the two planes intersect: They may be disjoint, meet at a point, or intersect along a line. In the first case, Voisin has shown that the associated K3 surfaces are isomorphic, but this is not true for generic members of the other two families.
Motivated by this observation, we discuss the geometry, Hodge theory and derived categories of K3 surfaces associated to a cubic fourfold containing two planes intersecting along a line. In particular, we interpret the twisted derived equivalence of these K3 surfaces as an instance of a theorem of Donagi and Pantev.
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