# Unimodal singularities and boundary divisors in the KSBA moduli of a class of Horikawa surfaces

### Luca Schaffler (Roma Tre University)

Wednesday 8th February 16:00-17:00 Maths 311B

#### Abstract

Smooth minimal surfaces of general type with $K^2=1$, $p_g=2$, and $q=0$ constitute a fundamental example in the geography of algebraic surfaces, and the 28-dimensional moduli space $\mathbf{M}$ of their canonical models admits a modular compactification $\overline{\mathbf{M}}$ via the minimal model program. We describe eight new irreducible boundary divisors in such compactification parametrizing reducible stable surfaces. Additionally, we study the relation with the GIT compactification of $\mathbf{M}$ and the Hodge theory of the degenerate surfaces that the eight divisors parametrize. This is joint work with Patricio Gallardo, Gregory Pearlstein, and Zheng Zhang.