Classification of order sixteen non-symplectic automorphisms on K3 surfaces

Dima Al Tabbaa; Alessandra Sarti; Shingo Taki

doi:10.4134/JKMS.j150339

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2016; 53(6): 1237-1260

Online first article October 14, 2016 Printed November 1, 2016

https://doi.org/10.4134/JKMS.j150339

Classification of order sixteen non-symplectic automorphisms on K3 surfaces

Dima Al Tabbaa, Alessandra Sarti, and Shingo Taki

T\'el\'eport 2, Boulevard Marie et Pierre Curie, T\'el\'eport 2, Boulevard Marie et Pierre Curie, Tokai University

Abstract

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Abstract

In the paper we classify complex K3 surfaces with non-sym\-plectic automorphism of order $16$ in full generality. We show that the fixed locus contains only rational curves and points and we completely classify the seven possible configurations. If the Picard group has rank 6, there are two possibilities and if its rank is 14, there are five possibilities. In particular if the action of the automorphism is trivial on the Picard group, then we show that its rank is six.

Keywords: non-symplectic automorphisms, K3 surfaces

MSC numbers: Primary 14J28; Secondary 14J50, 14J10