I‐surfaces from surfaces with one exceptional unimodal point

Sönke Rollenske and Diana Torres

Mathematische Nachrichten, 2024, vol. 297, issue 6, 2175-2197

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$E_{14}$.

Date: 2024
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