POINTED CURVES ON K3 SURFACES WHICH ARE DOUBLE COVERS OF RATIONAL ELLIPTIC SURFACES

Abstract

This article is a continuation of [4] in a way. We construct pointed curves on the K3 surfaces treated in [1] which are double covers of rational elliptic surfaces. In some cases we calculate the Weierstrass semigroups of the pointed curves. These pointed curves are the first examples on K3 surfaces that are double covers of rational elliptic surfaces such that we can calculate the Weierstrass semigroups. Moreover, we give bi-elliptic curves of genus 9 or 10 on some such K3 surfaces.