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: 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