Publicado

2018-01-01

Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles

Estabilización de los Grupos de Homotopía de los Espacios Móduli de los k-Fibrados de Higgs

DOI:

https://doi.org/10.15446/recolma.v1n52.74525

Palabras clave:

Moduli of Higgs Bundles, Variations of Hodge Structures, Vector Bundles (en)
Moduli de Fibrados de Higgs, Variaciones de Estructuras de Hodge, Fibrados Vectoriales (es)

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Autores/as

  • Ronald A. Zúñiga-Rojas Universidad de Costa Rica UCR
The work of Hausel proves that the Bialynicki-Birula stratification of the moduli space of rank two Higgs bundles coincides with its Shatz stratification. He uses that to estimate some homotopy groups of the moduli spaces of k-Higgs bundles of rank two. Unfortunately, those two stratifications do not coincide in general. Here, the objective is to present a different proof of the stabilization of the homotopy groups of Mk(2, d), and generalize it to Mk(3, d), the moduli spaces of k-Higgs bundles of degree d, and ranks two and three respectively, over a compact Riemann surface X, using the results from the works of Hausel and Thaddeus, among other tools.
El trabajo de Hausel prueba que la estratificación de Bialynicki-Birula del espacio moduli de fibrados de Higgs de rango dos coincide con su estratificación de Shatz. Él usa este hecho para calcular algunos grupos de homotopía del espacio moduli de k-fibrados de Higgs de rango dos. Desafortunadamente, estas dos estratificaciones no coinciden en general. Aquí, el objetivo es presentar una prueba diferente de la estabilización de los grupos de homotopía de Mk(2, d), y generalizarla a Mk(3, d), los espacios moduli de k-fibrados de Higgs de grado d, y rangos dos y tres respectivamente, sobre una superficie de Riemann compacta X, usando los resultados de los trabajos de Hausel y Thaddeus, entre otras herramientas.

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Cómo citar

APA

Zúñiga-Rojas, R. A. (2018). Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles. Revista Colombiana de Matemáticas, 52(1), 9–31. https://doi.org/10.15446/recolma.v1n52.74525

ACM

[1]
Zúñiga-Rojas, R.A. 2018. Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles. Revista Colombiana de Matemáticas. 52, 1 (ene. 2018), 9–31. DOI:https://doi.org/10.15446/recolma.v1n52.74525.

ACS

(1)
Zúñiga-Rojas, R. A. Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles. rev.colomb.mat 2018, 52, 9-31.

ABNT

ZÚÑIGA-ROJAS, R. A. Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles. Revista Colombiana de Matemáticas, [S. l.], v. 52, n. 1, p. 9–31, 2018. DOI: 10.15446/recolma.v1n52.74525. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/74525. Acesso em: 29 mar. 2024.

Chicago

Zúñiga-Rojas, Ronald A. 2018. «Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles». Revista Colombiana De Matemáticas 52 (1):9-31. https://doi.org/10.15446/recolma.v1n52.74525.

Harvard

Zúñiga-Rojas, R. A. (2018) «Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles», Revista Colombiana de Matemáticas, 52(1), pp. 9–31. doi: 10.15446/recolma.v1n52.74525.

IEEE

[1]
R. A. Zúñiga-Rojas, «Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles», rev.colomb.mat, vol. 52, n.º 1, pp. 9–31, ene. 2018.

MLA

Zúñiga-Rojas, R. A. «Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles». Revista Colombiana de Matemáticas, vol. 52, n.º 1, enero de 2018, pp. 9-31, doi:10.15446/recolma.v1n52.74525.

Turabian

Zúñiga-Rojas, Ronald A. «Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles». Revista Colombiana de Matemáticas 52, no. 1 (enero 1, 2018): 9–31. Accedido marzo 29, 2024. https://revistas.unal.edu.co/index.php/recolma/article/view/74525.

Vancouver

1.
Zúñiga-Rojas RA. Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles. rev.colomb.mat [Internet]. 1 de enero de 2018 [citado 29 de marzo de 2024];52(1):9-31. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/74525

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CrossRef Cited-by

CrossRef citations4

1. Alfonso Zamora Saiz, Ronald A. Zúñiga-Rojas. (2021). Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration. SpringerBriefs in Mathematics. , p.101. https://doi.org/10.1007/978-3-030-67829-6_6.

2. Alfonso Zamora Saiz, Ronald A. Zúñiga-Rojas. (2021). Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration. SpringerBriefs in Mathematics. , p.1. https://doi.org/10.1007/978-3-030-67829-6_1.

3. Ronald A. Zúñiga-Rojas. (2021). Variations of hodge structures of rank three k-Higgs bundles and moduli spaces of holomorphic triples. Geometriae Dedicata, 213(1), p.137. https://doi.org/10.1007/s10711-020-00572-0.

4. Peter B. Gothen, Ronald A. Zúñiga-Rojas. (2022). Stratifications on the nilpotent cone of the moduli space of Hitchin pairs. Revista Matemática Complutense, 35(2), p.311. https://doi.org/10.1007/s13163-021-00400-3.

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