SFU NTAG Seminar: Sarah Frei

Cubic fourfolds have been classically studied up to birational equivalence, with a view toward the rationality problem. The Fano variety of lines F(X) on a cubic fourfold X is a hyperkähler manifold, and the rationality of X is conjecturally captured by the geometry of F(X). In joint work with C. Brooke and L. Marquand, building on our previous work with X. Qin, we study pairs of conjecturally irrational cubic fourfolds with birational Fano varieties of lines. We provide new examples of pairs of cubic fourfolds with equivalent Kuznetsov components. Moreover, we show that the cubic fourfolds themselves are birational.