Lena Ji : The K-moduli space of a family of conic bundles

Posted by Gwyneth Moreland , part of the Algebraic Geometry Seminar.

At

Feb. 19, 2024, 3 p.m.

In

636 SEO

Abstract

In this talk, we study the 6-dimensional moduli space of a family of Fano threefolds, and we construct a compactification using K-stability. These threefolds admit a conic bundle structure---we relate the K-moduli space of the threefolds to the GIT moduli space of the discriminant curves, and we study the behavior of the conic bundle structure on the boundary. The technique we use is wall-crossings in K-moduli for certain log Fano pairs (X, cD) as the coefficient c varies. Our work is the first to systematically study these K-moduli spaces when D is not proportional to the anticanonical divisor of X, and we find surprising wall-crossing behavior in this setting. This work is joint with Kristin DeVleming, Patrick Kennedy-Hunt, and Ming Hao Quek.