The Weierstrass semigroups on double covers of genus two curves.

*(English)*Zbl 1316.14056A submonoid of non-negative integers is called a numerical semigroup if its complement is a finite set. The cardinality of the complement is called the genus. A numerical semigroup obtained by an algebraic curve and its point is called Weierstrass semigroup. A numerical semigroup is said to be of double covering type if it is obtained by an algebraic curve which is double covering of a curve and its ramification point. Numerical semigroups of double covering type obtained by double covering of curves of genus 0 and 1 were determined completely. In this paper, the authors determined numerical semigroups of double covering type obtained by double covering of curves of genus 2.

Reviewer: Takanori Ayano (Osaka)