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Double covers of Kummer surfaces

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Abstract

Besides its construction as a quotient of an abelian surface, a Kummer surface can be obtained as the quotient of a K3 surface by a \({\mathbb{Z}}/2{\mathbb{Z}}\) -action. In this paper, we classify all such K3 surfaces. Our classification is expressed in terms of period lattices and extends Morrison’s criterion of K3 surfaces with a Shioda–Inose structure. Moreover, we list all the K3 surfaces associated to a general Kummer surface and provide very geometrical examples of this phenomenon.

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  1. Section de Mathématiques, Université de Genève, 2-4 rue du Lièvre, Case Postale 64, 1211, Geneva 4, Switzerland

    Afsaneh Mehran

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  1. Afsaneh Mehran
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Mehran, A. Double covers of Kummer surfaces. manuscripta math. 123, 205–235 (2007). https://doi.org/10.1007/s00229-007-0092-4

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  • DOI: https://doi.org/10.1007/s00229-007-0092-4

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