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

Abstract

AbstractSmooth minimal surfaces of general type with , , and constitute a fundamental example in the geography of algebraic surfaces, and the 28‐dimensional moduli space of their canonical models admits a modular compactification 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 and the Hodge theory of the degenerate surfaces that the eight divisors parameterize.