ON GENERALIZED KUMMER SURFACES AND THE ORBIFOLD BOGOMOLOV-MIYAOKA-YAU INEQUALITY

摘要

A generalized Kummer surface X = Km(T, G) is the resolution of a quotient of a torus T by a finite group of symplectic automorphisms G. We complete the classification of generalized Kummer surfaces by studying the last two groups which have not been yet studied. For these surfaces we compute the associated Kummer lattice K-G, which is the minimal primitive sub-lattice containing the exceptional curves of the resolution X -> T/G. We then prove that a K3 surface is a generalized Kummer surface of type Km( T, G) if and only if its Neron-Severi group contains K-G.