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I‐surfaces from surfaces with one exceptional unimodal point

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  • Sönke Rollenske
  • Diana Torres

Abstract

We complement recent work of Gallardo, Pearlstein, Schaffler, and Zhang, showing that the stable surfaces with KX2=1$K_X^2 =1$ and χ(OX)=3$\chi (\mathcal {O}_X) = 3$ they construct are indeed the only ones arising from imposing an exceptional unimodal double point. In addition, we explicitly describe the birational type of the surfaces constructed from singularities of type E12$E_{12}$, E13$E_{13}$, E14$E_{14}$.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:mathna:v:297:y:2024:i:6:p:2175-2197
    DOI: 10.1002/mana.202300218
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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.
    2. 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.
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    2. 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.

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