I-surfaces from surfaces with one exceptional unimodal point

2023/05/02 by Sönke Rollenske, Rollenske, Sönke, Diana Torres +1
Mathematics · #14E05 #14J10 #14J29 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2305.01316

openalex publication_date 2023/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We complement recent work of Gallardo, Pearlstein, Schaffler, and Zhang, showing that the stable surfaces with K_X² =1 and χ(\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, E₁₃, and E₁₄.

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