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

André Contiero ^[1] ; Carlos Gustavo T. de A. Moreira ^[3] ; Paula M. Veloso ^[2]
1. [1] Universidade Federal de Alagoas
  
  Universidade Federal de Alagoas
  
  Brasil
2. [2] Universidade Federal Fluminense
  
  Universidade Federal Fluminense
  
  Brasil
3. [3] Instituto de Matemática Pura e Aplicada (IMPA), Brazil
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Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 9 (September 2015), 2015, págs. 3946-3957
Idioma: inglés
DOI: 10.1016/j.jpaa.2014.12.030
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Resumen
- 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.