On Weierstrass Gaps at Several Points

被引：0
作者：
Wanderson Tenório
Guilherme Tizziotti
机构：
[1] Universidade Federal de Uberlândia (UFU),Faculdade de Matemática
来源：
Bulletin of the Brazilian Mathematical Society, New Series | 2019年 / 50卷
关键词：
Weierstrass semigroup; Generalized Weierstrass semigroup; Pure gaps; Curves with separated variables;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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 (Proc Am Math Soc 108(3):627–631, 1990), we present a description of these elements which generalizes the approach of Homma and Kim (J Pure Appl Algebra 162(2–3):273–290, 2001) 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.
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页码：543 / 559
页数：16
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共 18 条
  • [1] Beelen P(2006)A generalization of the Weierstrass semigroup J. Pure Appl. Algebra 207 243-260
  • [2] Tutas N(2009)On Weierstrass semigroup and sets: a review with new results Geom. Dedicata 139 139-195
  • [3] Carvalho C(2005)On Goppa codes and Weierstrass gaps at several points Des. Codes Cryptogr. 35 211-225
  • [4] Kato T(1987)The semigroup of values of a curve singularity with several branches Manuscr. Math. 59 347-374
  • [5] Carvalho C(1990)The symmetry of the Weierstrass generalized semigroups and affine embeddings Proc. Am. Math. Soc. 108 627-631
  • [6] Torres F(2012)Delta sets for divisors supported in two points Finite Fields Appl. 18 865-885
  • [7] Delgado F(1996)The Weierstrass semigroup of a pair of points on a curve Arch. Math. 67 337-348
  • [8] Delgado F(2001)Goppa codes with Weierstrass pairs J. Pure Appl. Algebra 162 273-290
  • [9] Duursma IM(2018)Multi-point codes over Kummer extensions Des. Codes Cryptogr. 86 211-230
  • [10] Park S(2018)Pure Weierstrass gaps from a quotient of the Hermitian curve Finite Fields Appl. 50 251-271
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