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

2014/02/27 by Keum, JongHae
#14J28 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1402.6803

Abstract

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\nmid 66) and in the wild case (p=11).

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