On γ-Hyperelliptic Weierstrass Semigroups of Genus 6γ + 1 and 6γ

Let (C, P) be a pointed non-singular curve such that the Weierstrass semigroup H(P) of P is a γ-hyperelliptic numerical semigroup. Torres showed that there exists a double covering π : C → C‘ such that the point P is a ramification point of π if the genus g of C is larger than or equal to 6γ + 4. Kato and the authors also showed that the same result holds in the case g = 6γ + 3 or 6γ + 2. In this paper we prove that there exists a double covering π : C → C’ satisfying the above condition even if g = 6γ + 1, 6γ and H(P) does not contain 4.

This is a post-peer-review, pre-copyedit version of an article published in Bulletin of the Brazilian Mathematical Society, New Series. The final authenticated version is available online at: https://doi.org/10.1007/s00574-016-0002-z.