Fano schemes of singular symmetric matrices

Abstract: Fano schemes are moduli spaces that parameterize linear spaces contained in an embedded projective variety. In this talk, I investigate the Fano schemes parameterizing linear subspaces of symmetric matrices whose elements are all singular. I discuss their irreducibility, smoothness, and connectedness and show that they can have generically non-reduced components. As an application, I outline how to use the geometry of these schemes to give alternative arguments for several results on subspaces of singular symmetric matrices.

algebraic geometrynumber theory

Audience: researchers in the discipline

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.