Quotient spaces of K3 surfaces by non-symplectic involutions fixing a curve of genus 8 or more

Abstract

Abstract Let X be a K3 surface and let g be a non-symplectic involution of X such that the fixed points set contains a curve of genus 8 or more. In this paper, we show that the quotient space X/〈g〉 is determined by the fixed points set and the action of g on rational curves on X.