Explicit Nikulin configurations on Kummer surfaces

Abstract

Abstract A Nikulin configuration is the data of 16 disjoint smooth rational curves on a K3 surface. According to results of Nikulin, the existence of a Nikulin configuration means that the K3 surface is a Kummer surface, moreover the abelian surface from the Kummer structure is determined by the 16 curves. In the paper [16], we constructed explicitly non-isomorphic Kummer structures on some Kummer surfaces. In this paper we generalize the construction to Kummer surfaces with a weaker restriction on the degree of the polarization and we describe some cases where the previous construction does not work.