Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve (2112.08137v1)

Abstract: In this paper we determine the generalized Weierstrass semigroup $ \widehat{H}(P_{\infty}, P_1, \ldots , P_{m})$, and consequently the Weierstrass semigroup $H(P_{\infty}, P_1, \ldots , P_{m})$, at $m+1$ points on the curves $\mathcal{X}{a,b,n,s}$ and $\mathcal{Y}{n,s}$. These curves has been introduced in Tafazolian et al. as new examples of curves which cannot be covered by the Hermitian curve.