On Weierstrass gaps at several points

TL;DR

This paper generalizes the understanding of Weierstrass gaps at multiple points on algebraic curves by using the concept of relative maximality in generalized Weierstrass semigroups, extending previous pairwise approaches.

Contribution

It introduces a new description of Weierstrass gaps at several points using relative maximality, broadening the scope from pairs to multiple points on curves.

Findings

Provides a generalized framework for Weierstrass gaps at multiple points.

Applies the theory to a family of curves with separated variables.

Extends previous pairwise gap descriptions to multiple points.

Abstract

We consider the problem of determining Weierstrass gaps and pure Weierstrass gaps at several points. Using the notion of relative maximality in generalized Weierstrass semigroups due to Delgado \cite{D}, we present a description of these elements which generalizes the approach of Homma and Kim \cite{HK} given for pairs. Through this description, we study the gaps and pure gaps at several points on a certain family of curves with separated variables.