# Boundary divisors in the stable pair compactification of the moduli space of Horikawa surfaces – Luca Schaffler (Roma 3)

#### Venue

Dipartimento di Matematica, Aula Magna.

#### 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 $M$ of their canonical models admits a geometric and modular compactification $\overline{M}$ by stable surfaces. Franciosi-Pardini-Rollenske classified the Gorenstein stable degenerations parametrized by it, and jointly with Rana they determined boundary divisors parametrizing irreducible stable surfaces with a unique T-singularity. In this talk, we continue with the investigation of the boundary of $\overline{M}$ constructing eight new irreducible boundary divisors parametrizing reducible 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. This is joint work in progress with Patricio Gallardo, Gregory Pearlstein, and Zheng Zhang.

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