Bad irreducible subgroups and singular locus for character varieties in $PSL(p,\mathbb{C})$

Abstract

We describe the centralizer 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 (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 $l\ge 2$ or the fundamental group of a closed Riemann surface of genus $g\ge 2$, 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.

second version. 37 pages, 1 figure. The second version is much more focused, some proofs are omitted. A discussion on algebraic singularities has been added

Cited by in corpus (1)

• Bad Representations and Homotopy of Character Varieties