Anti-holomorphic involutions of the moduli spaces of Higgs bundles
Journal de l’École polytechnique - Mathématiques, Volume 2  (2015), p. 35-54

We study anti-holomorphic involutions of the moduli space of G-Higgs bundles over a compact Riemann surface X, where G is a complex semisimple Lie group. These involutions are defined by fixing anti-holomorphic involutions on both X and G. We analyze the fixed point locus in the moduli space and their relation with representations of the orbifold fundamental group of X equipped with the anti-holomorphic involution. We also study the relation with branes. This generalizes work by Biswas–García-Prada–Hurtubise and Baraglia–Schaposnik.

Nous étudions les involutions anti-holomorphes des espaces de modules de G-fibrés de Higgs sur une surface de Riemann compacte X, où G est un groupe de Lie semi-simple complexe. Ces involutions sont définies en fixant des involutions anti-holomorphes à la fois sur X et G. Nous en analysons le lieu des points fixes dans l’espace de modules et leur relation avec les représentation du groupe fondamental orbifold de X muni de l’involution anti-holomorphe. Nous étudions aussi la relation avec les « branes ». Ceci généralise les travaux de Biswas–García-Prada–Hurtubise et Baraglia–Schaposnik.

DOI : https://doi.org/10.5802/jep.16
Classification:  14H60,  57R57,  58D29
Keywords: Higgs G-bundle, reality condition, branes, character variety.
@article{JEP_2015__2__35_0,
     author = {Biswas, Indranil and Garc\'\i a-Prada, Oscar},
     title = {Anti-holomorphic involutions of the~moduli~spaces of Higgs bundles},
     journal = {Journal de l'\'Ecole polytechnique - Math\'ematiques},
     publisher = {Ecole polytechnique},
     volume = {2},
     year = {2015},
     pages = {35-54},
     doi = {10.5802/jep.16},
     language = {en},
     url = {http://www.numdam.org/item/JEP_2015__2__35_0}
}
Biswas, Indranil; García-Prada, Oscar. Anti-holomorphic involutions of the moduli spaces of Higgs bundles. Journal de l’École polytechnique - Mathématiques, Volume 2 (2015) , pp. 35-54. doi : 10.5802/jep.16. http://www.numdam.org/item/JEP_2015__2__35_0/

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