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On the Teichmüller stack of homogeneous spaces of SL2(C)

Abstract : Let Γ be a discrete torsion-free co-compact subgroup of SL2(C). E. Ghys has shown that the Kuranishi space of M = SL2(C)/Γ is given by the germ of the representation variety Hom(Γ, SL2(C)) at the trivial morphism and gave a description of the complex structures given by representations. In this note, we prove that for all admissible representations, i.e. which allow to construct compact complex manifold by this description, the representation variety (pointed at this representation), leads to a complete family even at singular points. Hence, we will consider the admissible character stack [R(Γ)^a / SL2(C)], where R(Γ)^a stands for the open subset formed by admissible representations with SL2(C) acting by conjugation on it and show that this quotient stack is an open substack of the Teichmüller stack of M.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03150275
Contributor : Théo Jamin Connect in order to contact the contributor
Submitted on : Tuesday, February 23, 2021 - 4:25:14 PM
Last modification on : Wednesday, October 20, 2021 - 3:19:01 AM
Long-term archiving on: : Monday, May 24, 2021 - 8:41:06 PM

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Théo Jamin. On the Teichmüller stack of homogeneous spaces of SL2(C). 2021. ⟨hal-03150275⟩

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