arXiv Open Access 2022

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

Patricio Gallardo Gregory Pearlstein Luca Schaffler Zheng Zhang

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Abstrak

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.

Topik & Kata Kunci

math.AG

Penulis (4)

Patricio Gallardo

Gregory Pearlstein

Luca Schaffler

Zheng Zhang

Format Sitasi

APA MLA BibTeX

Gallardo, P., Pearlstein, G., Schaffler, L., Zhang, Z. (2022). Unimodal singularities and boundary divisors in the KSBA moduli of a class of Horikawa surfaces. https://arxiv.org/abs/2209.08877

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Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓