T. Katsura

Title: Configurations of rational curves on supersingular K3 surfaces in small characteristics.

Abstract: Let C be a nonsingular complete curve of genus 2, and let J(C) be the Jacobian variety of C. If characteristic p is not equal to 2, then it is well-known that on the Kummer surface Km(J(C)), there exisits Kummer's 16_{6} configuration of 32 rational

curves. In this talk we consider the supersingular K3 surface with Artin invariant 1 in characteristic 2 (resp. 3). Using a structure of (generalized) Kummer surface, we show that on the surface there exists 21_{5} (resp. 16_{10}) configuration of 42 (resp. 32) rational curves. These facts relate to the structure of Leech lattice.