Projective models of the supersingular K3 surface with Artin invariant 1 in characteristic 5

Ichiro Shimada

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arXiv · 1201.4533

Projective models of the supersingular K3 surface with Artin invariant 1 in characteristic 5

Ichiro Shimada

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Abstract

Let X be a supersingular K3 surface in characteristic 5 with Artin invariant 1. Then X has a polarization that realizes X as the Fermat sextic double plane. We present a list of polarizations of X with degree 2 whose intersection number with this Fermat sextic polarization is less than or equal to 5, and give the defining equations of the corresponding projective models. We also present a method to describe birational morphisms between these projective models explicitly. As a by-product, a non-projective automorphism of the Fermat sextic double plane is obtained.

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BibTeX RIS

Ichiro Shimada. 2013-12-14. Projective models of the supersingular K3 surface with Artin invariant 1 in characteristic 5. https://arxiv.org/abs/1201.4533

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