Moduli spaces of Fano varieties can be singular

Abstract: Fano varieties are projective algebraic variety with “positive curvature”. Recently, using the notion of K-stability which originates in differential geometry, projective moduli spaces for Fano varieties have been constructed. In this talk I will show how to use polytopes and toric geometry (which is the study of certain algebraic varieties constructed in a combinatorial fashion) to produce singular points on these moduli spaces of Fano varieties. The talk is based on joint work with Anne-Sophie Kaloghiros.

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