Wall crossing for K-moduli spaces

Abstract: There are many different methods to compactly moduli spaces of varieties with a rich source of examples from compactifying moduli spaces of curves. In this talk, I will explain a relatively new compactification coming from K-stability and how it connects to serval other compactifications, focusing on the case of plane curves of degree $d$. In particular, we regard a plane curve as a log Fano pair $(\mathbb{P}^2, aC)$ and study the K-moduli compactifications and establish a wall crossing framework as a varies. We will describe all wall crossings for low degree plane curves and discuss the picture for general $\mathbb{Q}$-Gorenstein smoothable log Fano pairs. This is joint work with Kenneth Ascher and Yuchen Liu.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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