Luca Schaffler, Unimodal Singularities and Boundary Divisors in the KSBA Moduli of a Class of Horikawa Surfaces

Smooth minimal surfaces of general type with K²=1, p_g=2, and q=0 constitute a fundamental example in the geography of algebraic surfaces, and the 28-dimensional moduli space M of their canonical models admits a modular compactification 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 M and the Hodge theory of the degenerate surfaces that the eight divisors parametrize. Time permitting, we will discuss recent progress aimed at generalizing these techniques to study the boundary of compact moduli of other types of stable surfaces. This is joint work with Patricio Gallardo, Gregory Pearlstein, and Zheng Zhang.