Non-symplectic automorphisms of K3 surfaces with one-dimensional moduli space

• Michela Artebani ^[1] ; Paola Comparin ^[2] ; María Elisa Valdés ^[1]
  1. [1] Universidad de Concepción

     Universidad de Concepción

     Comuna de Concepción, Chile

     
  2. [2] Universidad de La Frontera

     Universidad de La Frontera

     Temuco, Chile

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 4, 2022, págs. 1161-1198
• Idioma: inglés
• DOI: 10.4171/RMI/1326
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• Resumen

  • The moduli space of K3 surfaces XX with a purely non-symplectic automorphism \sigmaσ of order n\geq 2n≥2 is one dimensional exactly when \varphi(n)=8φ(n)=8 or 1010. In this paper we classify and give explicit equations for the very general members (X,\sigma)(X,σ) of the irreducible components of maximal dimension of such moduli spaces. In particular, we show that there is a unique one-dimensional component for n=20,22, 24n=20,22,24, three irreducible components for n=15n=15 and two components in the remaining cases.