Weierstrass semigroup and Automorphism group of the curves $\mathcal{X}_{n,r}$

TL;DR

This paper determines the Weierstrass semigroup and automorphism group of a specific family of algebraic curves, providing new insights into their structure and symmetries.

Contribution

It explicitly computes the Weierstrass semigroup and automorphism group for the curves $\

Findings

Weierstrass semigroup $H(P_{})$ characterized.

Full automorphism group of $\

New structural properties of $\

Abstract

In this paper, we determine the Weierstrass semigroup $H(P_{\infty})$ and the full automorphism group of a certain family of curves $\mathcal{X}_{n,r}$, which was recently introduced by Borges and Concei\c{c}\~ao.