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

Patricio Gallardo, Gregory Pearlstein, Luca Schaffler and Zheng Zhang

Mathematische Nachrichten, 2024, vol. 297, issue 2, 595-628

Abstract: Smooth minimal surfaces of general type with K2=1$K^2=1$, pg=2$p_g=2$, and q=0$q=0$ constitute a fundamental example in the geography of algebraic surfaces, and the 28‐dimensional moduli space M$\mathbf {M}$ of their canonical models admits a modular compactification M¯$\overline{\mathbf {M}}$ via the minimal model program. We describe eight new irreducible boundary divisors in such compactification parameterizing reducible stable surfaces. Additionally, we study the relation with the GIT compactification of M$\mathbf {M}$ and the Hodge theory of the degenerate surfaces that the eight divisors parameterize.

Date: 2024
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