Publicado

2017-07-01

Morfismos de Abel, series lineales y sus límites sobre curvas

Abel maps, linear series and their limits on curves

DOI:

https://doi.org/10.15446/recolma.v51n2.70895

Palabras clave:

Series lineales, morfismos de Abel, series lineales límite, espacios moduli (es)
Linear series, Abel maps, limit linear series, moduli spaces (en)

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Autores/as

  • Pedro H. Rizzo Universidad de Antioquia
Se presentan los principales resultados y técnicas en la construcción de los espacios moduli de series lineales, series lineales límite sobre curvas y la relación de estos con los morfismos de Abel. Se inicia con una breve revisión de la teoría de series lineales y sus principales consecuencias sobre curvas suaves. Son examinadas dos construcciones de límites de series lineales y sus espacios moduli: los de tipo Eisenbud-Harris [14] y los de tipo Osserman [42]. Adicionalmente, es presentada la relación de esta última construcción con las fibras de los morfismos de Abel [22] y así mismo la construcción de los límites del tipo Esteves-Nigro-Rizzo [20, 21] que generalizan los dos tipos de límites anteriores. Finalmente, una breve digresión presenta los avances actuales y aspectos de futuros desarrollos relacionados a estas teorías y sus aplicaciones.
We introduce the main results and techniques related to the constructions of the moduli spaces of linear series, limit linear series on curves and its relations with Abel maps. We start with a brief exposition of the theory of the linear series and its main consequences on smooth curves. Also, we examine two constructions of limits of linear series and their moduli spaces: Eisenbud and Harris types [14] and Osserman types [42]. In addition, we discuss the relation of the latter construction with Abel maps [22] and we present a new limits construction: Esteves-Nigro-Rizzo types [20, 21] which generalize Eisenbud{Harris and Osserman constructions. Finally, we give a brief overview on further works related to these theories and their applications.

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Cómo citar

APA

H. Rizzo, P. (2017). Morfismos de Abel, series lineales y sus límites sobre curvas. Revista Colombiana de Matemáticas, 51(2), 119–152. https://doi.org/10.15446/recolma.v51n2.70895

ACM

[1]
H. Rizzo, P. 2017. Morfismos de Abel, series lineales y sus límites sobre curvas. Revista Colombiana de Matemáticas. 51, 2 (jul. 2017), 119–152. DOI:https://doi.org/10.15446/recolma.v51n2.70895.

ACS

(1)
H. Rizzo, P. Morfismos de Abel, series lineales y sus límites sobre curvas. rev.colomb.mat 2017, 51, 119-152.

ABNT

H. RIZZO, P. Morfismos de Abel, series lineales y sus límites sobre curvas. Revista Colombiana de Matemáticas, [S. l.], v. 51, n. 2, p. 119–152, 2017. DOI: 10.15446/recolma.v51n2.70895. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/70895. Acesso em: 29 mar. 2024.

Chicago

H. Rizzo, Pedro. 2017. «Morfismos de Abel, series lineales y sus límites sobre curvas». Revista Colombiana De Matemáticas 51 (2):119-52. https://doi.org/10.15446/recolma.v51n2.70895.

Harvard

H. Rizzo, P. (2017) «Morfismos de Abel, series lineales y sus límites sobre curvas», Revista Colombiana de Matemáticas, 51(2), pp. 119–152. doi: 10.15446/recolma.v51n2.70895.

IEEE

[1]
P. H. Rizzo, «Morfismos de Abel, series lineales y sus límites sobre curvas», rev.colomb.mat, vol. 51, n.º 2, pp. 119–152, jul. 2017.

MLA

H. Rizzo, P. «Morfismos de Abel, series lineales y sus límites sobre curvas». Revista Colombiana de Matemáticas, vol. 51, n.º 2, julio de 2017, pp. 119-52, doi:10.15446/recolma.v51n2.70895.

Turabian

H. Rizzo, Pedro. «Morfismos de Abel, series lineales y sus límites sobre curvas». Revista Colombiana de Matemáticas 51, no. 2 (julio 1, 2017): 119–152. Accedido marzo 29, 2024. https://revistas.unal.edu.co/index.php/recolma/article/view/70895.

Vancouver

1.
H. Rizzo P. Morfismos de Abel, series lineales y sus límites sobre curvas. rev.colomb.mat [Internet]. 1 de julio de 2017 [citado 29 de marzo de 2024];51(2):119-52. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/70895

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