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On Büchi’s K3 surface

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Abstract

We study the Büchi K3 surface proving that it belongs to the one dimensional family of Kummer surfaces associated to genus two curves with automorphism group \(D_4\). We compute its Picard lattice and show that the rational points of the surface are Zariski-dense. Moreover, we provide analogous results for the Kummer surface associated to any genus two curve whose automorphism group contains a non-hyperelliptic involution.

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Acknowledgments

We thank the anonymous referee for carefully reading our paper and for suggesting to look at families of lattice polarized K3 surfaces. We would also like to thank Daniel Huybrechts, Kieran O’Grady, Héctor Pastén, Alessandra Sarti, Matthias Schütt, Pol Vanhaecke and Xavier Vidaux for comments on a preliminary version of this paper.

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Authors and Affiliations

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

    Michela Artebani & Antonio Laface

  2. Mathematics Institute, Zeeman Building, University of Warwick, Coventry, CV4 7AL, UK

    Damiano Testa

Authors
  1. Michela Artebani
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  2. Antonio Laface
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  3. Damiano Testa
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Correspondence to Damiano Testa.

Additional information

The first author has been partially supported by Proyecto FONDECYT Regular N. 1110249 and Proyecto FONDECYT Regular N. 1130572. The second author has been partially supported by Proyecto FONDECYT Regular N. 1110096. The third author has been partially supported by EPSRC grant EP/F060661/1 and by EPSRC grant EP/K019279/1.

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Artebani, M., Laface, A. & Testa, D. On Büchi’s K3 surface. Math. Z. 278, 1113–1131 (2014). https://doi.org/10.1007/s00209-014-1348-9

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  • DOI: https://doi.org/10.1007/s00209-014-1348-9

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