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

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  • Patricio Gallardo
  • Gregory Pearlstein
  • Luca Schaffler
  • Zheng Zhang

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.

Suggested Citation

  • Patricio Gallardo & Gregory Pearlstein & Luca Schaffler & Zheng Zhang, 2024. "Unimodal singularities and boundary divisors in the KSBA moduli of a class of Horikawa surfaces," Mathematische Nachrichten, Wiley Blackwell, vol. 297(2), pages 595-628, February.
    • Handle: RePEc:bla:mathna:v:297:y:2024:i:2:p:595-628
    DOI: 10.1002/mana.202300019
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    References listed on IDEAS

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    1. Marco Franciosi & Rita Pardini & Sönke Rollenske, 2017. "Gorenstein stable surfaces with K X 2 = 1 and p g > 0," Mathematische Nachrichten, Wiley Blackwell, vol. 290(5-6), pages 794-814, April.
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    Cited by:

    1. Sönke Rollenske & Diana Torres, 2024. "I‐surfaces from surfaces with one exceptional unimodal point," Mathematische Nachrichten, Wiley Blackwell, vol. 297(6), pages 2175-2197, June.

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