On the structure of numerical sparse semigroups and applications to Weierstrass points

2013/08/27 by André Contiero, Contiero, André, Carlos Gustavo T. A. Moreira +3
Computer Science · Engineering · Mathematics · #14H55 #20M13 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14H55 #msc:20M13

paper · pdf · doi:10.48550/arxiv.1308.5844

to appear in Journal of Pure and Applied Algebra

openalex publication_date 2013/08/27 · arxiv created 2014/10/13 · arxiv updated 2014/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we are concerned with the structure of sparse semigroups and some applications of them to Weierstrass points. We manage to describe, classify and find an upper bound for the genus of sparse semigroups. We also study the realization of some sparse semigroups as Weierstrass semigroups. The smoothness property of monomial curves associated to (hyper)ordinary semigroups presented by Pinkham and Rim-Vitulli, and the results on double covering of curves by Torres are crucial in this.

Related

• Remarks on numerical semigroups
• The Weierstrass semigroups on double covers of genus two curves
• Weierstrass semigroups at every point of the Suzuki curve
• Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve
• Irreducibility and stable rationality of the loci of Weierstrass points on curves of genus at most six