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Mori dream K3 surfaces of Picard number four: projective models and Cox rings

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Abstract

In this paper we study the geometry of the 14 families of K3 surfaces of Picard number four with finite automorphism group, whose Neron—Severi lattices have been classified by È. B. Vinberg. We provide projective models, we identify the degrees of a generating set of the Cox ring and in some cases we prove the unirationality of the associated moduli space.

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Authors and Affiliations

  1. Departamento de Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Michela Artebani

  2. Departamento de Matemática, Universidad de Tarapacá, Casilla 6-D, Arica, Chile

    Claudia Correa Deisler

  3. Institut Archimède Mathématiques-Informatique, Aix-Marseille Université, CNRS, Centrale Marseille, I2M UMR 7373, 13453, Marseille, France

    Xavier Roulleau

Authors
  1. Michela Artebani
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  2. Claudia Correa Deisler
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  3. Xavier Roulleau
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Corresponding author

Correspondence to Xavier Roulleau.

Additional information

The authors have been partially supported by Proyecto FONDECYT Regular N. 1160897 and N. 1211708 and by Proyecto Anillo ACT 1415 PIA CONICYT (first and second author). The second author has been supported by CONICYT PCHA/DoctoradoNacional/2012/21120687.

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Artebani, M., Deisler, C.C. & Roulleau, X. Mori dream K3 surfaces of Picard number four: projective models and Cox rings. Isr. J. Math. 258, 81–135 (2023). https://doi.org/10.1007/s11856-023-2469-9

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  • DOI: https://doi.org/10.1007/s11856-023-2469-9

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