English

On the Teichm\"uller stack of homogeneous spaces of SL(2,C)

Algebraic Geometry 2021-02-25 v1 Complex Variables Representation Theory

Abstract

In this paper, we show that the (admissible) character stack, which is a stack version of the character variety, is an open substack of the Teichm\"uller stack of homogeneous spaces of SL(2,C). We show that the tautological family over the representation variety, given by deforming the holonomy, is always a complete family. This is a generalisation of the work of E. Ghys about deformations of complex structures these homogeneous spaces.

Keywords

Cite

@article{arxiv.2102.12364,
  title  = {On the Teichm\"uller stack of homogeneous spaces of SL(2,C)},
  author = {Théo Jamin},
  journal= {arXiv preprint arXiv:2102.12364},
  year   = {2021}
}