| Autor: |
Tholozan, Nicolas, Toulisse, Jérémy |
| Rok vydání: |
2018 |
| Předmět: |
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| Zdroj: |
Ãpijournal de Géométrie Algébrique, Volume 5 (April 19, 2021) epiga:5894 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.46298/epiga.2021.volume5.5894 |
| Popis: |
We prove that some relative character varieties of the fundamental group of a punctured sphere into the Hermitian Lie groups $\mathrm{SU}(p,q)$ 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 $\textrm{PU}(1,1) = \mathrm{PSL}(2,\mathbb{R})$. 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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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