##### Department of Mathematics,

University of California San Diego

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### PhD Thesis Defense

## Jacob Keller

#### UC San Diego

## The Birational Geometry of K-Moduli Spaces

##### Abstract:

For $C$ a smooth curve and $\xi$ a line bundle on $C$, the moduli space $U_C(2,\xi)$ of semistable vector bundles of rank two and determinant $\xi$ is a Fano variety. We show that $U_C(2,\xi)$ is K-stable for a general curve $C \in \overline{M}_g$. As a consequence, there are irreducible components of the moduli space of K-stable Fano varieties that are birational to $\overline{M}_g$. In particular these components are of general type for $g\geq 22$.

Advisor: James McKernan

### May 31, 2024

### 9:30 AM

AP&M 7321

Zoom link: https://ucsd.zoom.us/j/

Research Areas

Algebraic Geometry****************************