Abelian surface fibrations and lines on cubic fourfolds

Abstract: If X is a cubic fourfold (i.e. a hypersurface of degree three in P^5), then its Fano variety of lines F is an irreducible symplectic variety of dimension four. Over the complex numbers, tools from hyperkähler geometry reveal that F only admits a nontrivial morphism to a lower-dimensional variety when X contains certain "special" algebraic surfaces. In this talk, we consider the case when X contains a plane: it turns out that F is birational to another irreducible symplectic variety admitting a morphism to P^2 whose general fiber is an abelian surface. We will show the key geometric ingredients involved in this construction and describe some of its arithmetic when the ground field is not closed.

algebraic geometrynumber theory

Audience: researchers in the topic

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