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: Description: Research/departmental seminar

Seminar usually meets in-person. For online editions, the Zoom link is shared via mailing list.