Singularités orbifoldes de la variété des caractères

In this thesis, we want to understand some singularities in the character variety. In a first chapter, we justify that the characters of irreducible representations from a Fuchsian group to a complex semi-simple Lie group is an orbifold. The orbifold locus is, then, the characters of bad representations. In the second chapter, we focus on the case where the Lie group is PSL(p,C) with p a prime number. In particular we give an explicit description of this locus. In the third and fourth chapter, we describe the isotropy groups (i.e. the centralizers of bad subgroups) arising in the cases when the Lie group is a quotient SL(n,C) (third chapter) and when the Lie group is a quotient of Spin(n,C) in the fourth chapter.