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Nikulin involutions on K3 surfaces

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Abstract

We study the maps induced on cohomology by a Nikulin (i.e. a symplectic) involution on a K3 surface. We parametrize the 11-dimensional irreducible components of the moduli space of algebraic K3 surfaces with a Nikulin involution and we give examples of the general K3 surface in various components. We conclude with some remarks on Morrison–Nikulin involutions, these are Nikulin involutions which interchange two copies of E 8(−1) in the Néron Severi group.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Milano, via Saldini 50, 20133, Milan, Italy

    Bert van Geemen & Alessandra Sarti

  2. Institut für Mathematik, Universität Mainz, Staudingerweg 9, 55099, Mainz, Germany

    Alessandra Sarti

Authors
  1. Bert van Geemen
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  2. Alessandra Sarti
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Correspondence to Alessandra Sarti.

Additional information

The second author is supported by DFG Research Grant SA 1380/1-1.

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van Geemen, B., Sarti, A. Nikulin involutions on K3 surfaces. Math. Z. 255, 731–753 (2007). https://doi.org/10.1007/s00209-006-0047-6

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  • DOI: https://doi.org/10.1007/s00209-006-0047-6

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