On Weierstrass semigroups of double coverings of genus three curves

Abstract

Let C be a complete non-singular curve of genus 3 over an algebraically closed field of characteristic 0. We determine all possible Wierstrass semigroups of ramification points on double coverings of C whose covering curves have genus greater than 8. Moreover, we construct double coverings with ramification points whose Weierstrass semigroups are the possible ones.