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

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.Comment: 31 page

Note on tautological classes of moduli of K3 surfaces

We prove some cycle relations on moduli of K3 surfacesComment: 5 page