K3 surfaces with an automorphism of order 66, the maximum possible

In each characteristic p≠2,3, it was shown in a previous work that the order of an automorphism of a K3 surface is bounded by 66, if finite. Here, it is shown that in each characteristic p≠2,3 a K3 surface with a cyclic action of order 66 is unique up to isomorphism. The equation of the unique surfa...

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Bibliographic Details
Published inJournal of algebra Vol. 426; pp. 273 - 287
Main Author Keum, JongHae
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.03.2015
Subjects
Automorphism
K3 surfaces
Automorphism
K3 surfaces
primary
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Summary:In each characteristic p≠2,3, it was shown in a previous work that the order of an automorphism of a K3 surface is bounded by 66, if finite. Here, it is shown that in each characteristic p≠2,3 a K3 surface with a cyclic action of order 66 is unique up to isomorphism. The equation of the unique surface is given explicitly in the tame case (p∤66) and in the wild case (p=11).
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2014.12.018