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Abstract des Vortrages von Toshiyuki Katsura

Configurations of smooth rational curves on superspecial K3 surfaces in small characteristics

Let C be a nonsingular complete curve of genus 2, and let J(C) be the Jacobian variety of C. If the 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 smooth rational curves. In this talk we consider supersingular K3 surfaces with Artin invariant 1 in characteristic 2, 3 and 5. Using the theory of abelian surface, we show that on these surfaces there exist various interesting configurations of smooth rational curves, and that these facts relate to the structure of Leech lattice.