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Department of Mathematics,
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****************************
