Mathematical Research Letters

Volume 21 (2014)

Number 3

$\mathrm{K}3$ surfaces with an order 60 automorphism and a characterization of supersingular $\mathrm{K}3$ surfaces with Artin invariant $1$

Pages: 509 – 520

DOI: http://dx.doi.org/10.4310/MRL.2014.v21.n3.a8

Author

Jonghae Keum (School of Mathematics, Korea Institute for Advanced Study, Seoul, Korea)

Abstract

In characteristic $p = 0$ or $p \gt 5$, we show that a $\mathrm{K}3$ surface with an order 60 automorphism is unique up to isomorphism. As a consequence, we characterize the supersingular $\mathrm{K}3$ surface with Artin invariant $1$ in characteristic $p \equiv 11$ (mod $12$) by a cyclic symmetry of order 60.

2010 Mathematics Subject Classification

14J27, 14J28, 14J50

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