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

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

2011-07-08

arxiv.org/abs/1107.1543v1

Mathematics

Algebraic Geometry

31 pages

Scientific paper

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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