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.
Gallardo, P., Pearlstein, G., Schaffler, L., Zhang, Z. (2024). Unimodal singularities and boundary divisors in the KSBA moduli of a class of Horikawa surfaces. MATHEMATISCHE NACHRICHTEN [10.1002/mana.202300019].
Unimodal singularities and boundary divisors in the KSBA moduli of a class of Horikawa surfaces
Pearlstein G.;Schaffler L.
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2024-01-01
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 $\mathbf{M}$ 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.