# On Weierstrass semigroup at $m$ points on curves of the type f(y) = g(x)

## TL;DR

This paper determines the minimal generating set of the Weierstrass semigroup at multiple points on certain algebraic curves with a specific plane model, using the concept of discrepancy to generalize previous methods.

## Contribution

It introduces a new approach using discrepancy to compute Weierstrass semigroups at multiple points on curves of the form f(y)=g(x), broadening the scope beyond specific cases.

## Key findings

- Explicit minimal generating sets for the semigroup at multiple points.
- Application of discrepancy concept to a broader class of curves.
- Generalization of previous methods to new curve types.

## Abstract

In this work we determine the so-called minimal generating set of the Weierstrass semigroup of certain $m$ points on curves $\mathcal{X}$ with plane model of the type $f(y) = g(x)$ over $\mathbb{F}_{q}$, where $f(T),g(T)\in \mathbb{F}_q[T]$. Our results were obtained using the concept of discrepancy, for given points $P$ and $Q$ on $\mathcal{X}$. This concept was introduced by Duursma and Park, in \cite{duursma}, and allows us to make a different and more general approach than that used to certain specific curves studied earlier.