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

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.

31 pages

References in corpus (1)

• A note on a supersingular K3 surface in characteristic 2