Cubic fourfolds with birational Fano varieties of lines

Abstract: 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.

algebraic geometrynumber theory

Audience: researchers in the discipline

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca