##### Department of Mathematics,

University of California San Diego

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### Math 208 - Algebraic Geometry

## Kristin DeVleming

#### UCSD

## Wall crossing for K-moduli spaces of plane curves

##### Abstract:

I will discuss compactifications of the moduli space of smooth plane curves of degree d at least 4. We will regard a plane curve as a log Fano pair $(\mathbb{P}^2,aC)$, where a is a rational number, and study the compactifications coming from K stability for general log Fano pairs. We establish a wall crossing framework to study these spaces as a varies and show that, when a is small, the moduli space coming from K stability is isomorphic to the GIT moduli space. We describe all wall crossings for degree 4, 5, and 6 plane curves and discuss the picture for general Q-Gorenstein smoothable log Fano pairs. This is joint work with Kenneth Ascher and Yuchen Liu.

Host: James McKernan

### January 24, 2020

### 3:00 PM

### AP&M 7321

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