Curves on weighted K3 surfaces of degree two with symmetric Weierstrass semigroups

Abstract

Let $C$ be a curve on the weighted projective plane $\mathbf{P}(1, 1, 4)$ which is of Fermat type or almost Fermat type. We construct K3 surfaces which are double covers of $\mathbf{P}(1, 1, 4)$ and which contain pointed curves with symmetric Weierstrass semigroups which are double covers of $C$.