Seminari del Dipartimento
Geometria Unimodal singularities and boundary divisors in the KSBA moduli of a class of Horikawa surfaces Luca Schaffler 29-09-2022 - 14:15 Largo San Leonardo Murialdo, 1
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. |