Vanishing Brauer Classes

Location: 11th Floor Lecture Hall Speaker Federica Galluzzi, University of Turin Session Chair Asher Auel, Dartmouth College Abstract A cubic fourfold X in P^5 containing a plane P defines, via projection from P, a quadric surface bundle over P^2 whose discriminant curve C is a plane sextic. A specialization of such a cubic fourfold in which the rank of the group of codimension two cycles increases from two to three induces a specialization of the K3 double plane S defined by X, and hence defines a vanishing Brauer class of order two in Br(S). In this talk, based on joint work with Bert van Geemen, I will describe the B-field invariants of the vanishing Brauer class, determine whether this class corresponds to a 2-torsion point in J(C) or to an even or odd theta characteristic on C and clarify the relation to the natural Clifford class defined by (X,P). I will then discuss some explicit examples related to Verra fourfolds.