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Article Dans Une Revue Épijournal de Géométrie Algébrique Année : 2021

Compact Connected Components In Relative Character Varieties Of Punctured Spheres

Résumé

We prove that some relative character varieties of the fundamental group of a punctured sphere into the Hermitian Lie groups SU(p, q) admit compact connected components. The representations in these components have several counter-intuitive properties. For instance, the image of any simple closed curve is an elliptic element. These results extend a recent work of Deroin and the first author, which treated the case of PU(1, 1) = PSL(2, R). Our proof relies on the non-Abelian Hodge correspondance between relative character varieties and parabolic Higgs bundles. The examples we construct admit a rather explicit description as projective varieties obtained via Geometric Invariant Theory.
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Dates et versions

hal-02419935 , version 1 (19-12-2019)

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Nicolas Tholozan, Jérémy Toulisse. Compact Connected Components In Relative Character Varieties Of Punctured Spheres. Épijournal de Géométrie Algébrique, 2021, ⟨10.46298/epiga.2021.volume5.5894⟩. ⟨hal-02419935⟩
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