Moduli of Higgs bundles over the five punctured sphere
| Autor: | Fassarella, Thiago, Loray, Frank |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | We look at rank two parabolic Higgs bundles over the projective line minus five points which are semistable with respect to a weight vector $\mu\in[0,1]^5$. The moduli space corresponding to the central weight $\mu_c=(\frac{1}{2}, \dots, \frac{1}{2})$ is studied in details and all singular fibers of the Hitchin map are described, including the nilpotent cone. After giving a description of fixed points of the $\mathbb C^*$-action we obtain a proof of Simpson's foliation conjecture in this case. For each $n\ge 5$, we remark that there is a weight vector so that the foliation conjecture in the moduli space of rank two logarithmic connections over the projective line minus $n$ points is false. Comment: 27 pages, 6 figures |
| Databáze: | arXiv |
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