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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.53 supl.1 Bogotá Dec. 2019 Epub Mar 24, 2020
https://doi.org/10.15446/recolma.v53nsupl.84089
Artículos originales
On space maximal curves
Sobre curvas maximales en el espacio
1 Universidade Regional do Cariri, Brazil
2 Universidade Estadual de Campinas, Brazil
Any maximal curve X is equipped with an intrinsic embedding π: X → ℙr which reveal outstanding properties of the curve. By dealing with the contact divisors of the curve π(X) and tangent lines, in this paper we investigate the first positive element that the Weierstrass semigroup at rational points can have whenever r = 3 and π(X) is contained in a cubic surface.
Keywords: finite fields; Stöhr-Voloch theory; Hasse-Weil bound; maximal curve
Toda curva maximal X está intrínsicamente dotada de un mergullo π: X → ℙr el cual vislumbra propiedades cruciales de la curva. Para r = 3, considerando los divisores de contacto de la curva π(X) y rectas tangentes, investigamos el posible primer elemento positivo que un semigrupo de Weierstrass en un punto racional puede tener en el caso que π(X) esté contenida en una superficie cúbica.
Palabras clave: finitos; teoría de Stöhr-Voloch; cota de Hasse-Weil; curva maximal
Acknowledgment.
This paper is based on the Ph.D. dissertation [20] done at IMECC-UNICAMP. The second author was partially supported by CNPq (Grant 310623/2017-0). We also gratefully thank James W.P. Hirschfeld for useful comments.
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Received: August 07, 2018; Accepted: November 16, 2018
Todo el contenido de esta revista, excepto dónde está identificado, está bajo una Licencia Creative Commons BY
