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arXiv · 1107.1543

Rational curves on the supersingular K3 surface with Artin invariant 1 in characteristic 3

Toshiyuki Katsura·Shigeyuki Kondo
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Abstract

We show the existence of 112 non-singular rational curves on the supersingular K3 surface with Artin invariant 1 in characteristic 3 by several ways. Using these rational curves, we have a $(16)_{10}$-configuration and a $(280_{4}, 112_{10})$-configuration on the K3 surface. Moreover we study the Picard lattice by using the theory of the Leech lattice. The 112 non-singular rational curves correspond to 112 Leech roots.

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Toshiyuki Katsura, Shigeyuki Kondo. 2011-07-08. Rational curves on the supersingular K3 surface with Artin invariant 1 in characteristic 3. https://arxiv.org/abs/1107.1543

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