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arXiv · 1906.02616

Symmetries of order eight on K3 surfaces without high genus curves in the fixed locus

Dima Al Tabbaa·Annalisa Grossi·Alessandra Sarti
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Abstract

In this paper we classify non-symplectic automorphisms of order 8 on complex K3 surfaces in case that the fourth power of the automorphism has only rational curves in its fixed locus. We show that the fixed locus is the disjoint union of a rational curve and 10 isolated points or it consists in 4 isolated fixed points. We give examples corresponding to the case with a rational curve in the fixed locus and to the case with only isolated points in the fixed locus.

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Dima Al Tabbaa, Annalisa Grossi, Alessandra Sarti. 2020-01-02. Symmetries of order eight on K3 surfaces without high genus curves in the fixed locus. https://arxiv.org/abs/1906.02616

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