Reference : Bad irreducible subgroups and singular locus for character varieties in PSL(p,C)
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/29138
Bad irreducible subgroups and singular locus for character varieties in PSL(p,C)
English
Guerin, Clément mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Aug-2017
Geometriae Dedicata
Springer Netherlands
Yes (verified by ORBilu)
International
0046-5755
1572-9168
Dordrecht
The Netherlands
[en] Character variety ; Centralizers of irreducible representations ; Fuchsian groups representations
[en] We give the centralizers of irreducible representations from a finitely generated group $\Gamma$ to $PSL(p,\mathbb{C})$ where p is a prime number. This leads to a description of the singular locus (te (the set of conjugacy classes of representations whose centralizer strictly contains the center of the ambient group) of the irreducible part of the character variety $\chi^i(\Gamma,PSL(p,\mathbb{C}))$. When $\Gamma$ is a free group of rank $l\geq 2$ or the fundamental group of a closed Riemann surface of genus $g\geq 2$, we give a complete description of this locus and prove that this locus is exactly the set of algebraic singularities of the irreducible part of the character variety.
Researchers
http://hdl.handle.net/10993/29138
10.1007/s10711-017-0275-4
https://doi.org/10.1007/s10711-017-0275-4

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