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K3 surfaces with non-symplectic automorphisms of prime order

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With an appendix by Shigeyuki Kondō

Abstract

In this paper we present the classification of non-symplectic automorphisms of prime order on K3 surfaces, i.e. we describe the topological structure of their fixed locus and determine their invariant lattice in cohomology. We provide new results for automorphisms of order 5 and 7 and alternative proofs for higher orders. Moreover, for any prime p, we identify the irreducible components of the moduli space of K3 surfaces with a non-symplectic automorphism of order p.

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Authors and Affiliations

  1. Departamento de Matemática, Universidad de Concepción, Casilla160-C, Concepción, Chile

    Michela Artebani

  2. Laboratoire de Mathématiques et Applications, Université de Poitiers, Téléport 2 Boulevard Marie et Pierre Curie, BP 30179, 86962, Futuroscope Chasseneuil Cedex, France

    Alessandra Sarti

  3. Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Japan

    Shingo Taki

Authors
  1. Michela Artebani
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  2. Alessandra Sarti
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  3. Shingo Taki
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Correspondence to Michela Artebani.

Additional information

M. Artebani has been partially supported by Proyecto FONDECYT Regular 2009, N. 1090069. S. Kondō’s research was partially supported by Grant-in-Aid for Scientific Research A-18204001 and Houga-20654001, Japan.

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Artebani, M., Sarti, A. & Taki, S. K3 surfaces with non-symplectic automorphisms of prime order. Math. Z. 268, 507–533 (2011). https://doi.org/10.1007/s00209-010-0681-x

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