Coordinate rings of some $SL_2$-character varieties

Vicente Muñoz; Jesús Martín Ovejero

paper

Coordinate rings of some $S L_{2}$ -character varieties

arXiv:2202.07227

Abstract

We determine generators of the coordinate ring of $S L_{2}$ -character varieties. In the case of the free group $F_{3}$ we obtain an explicit equation of the $S L_{2}$ -character variety. For free groups $F_{k}$ we find transcendental generators. Finally, for the case of the 2-torus, we get an explicit equation of the $S L_{2}$ -character variety and use the description to compute their E-polynomials.

16 pages, no figures; v2. References added

Coordinate rings of some SL2​-character varieties

Abstract

Coordinate rings of some $S L_{2}$ -character varieties