Coordinate rings of some $\mathrm{SL}_2$-character varieties

Authors

  • Vicente Muñoz Departamento de Álgebra, Geometría y Topología, Facultad de Ciencias, Universidad de Málaga, Campus de Teatinos s/n, 29071 Málaga, Spain
  • Jesús Martín Ovejero Departamento de Mátemáticas, Facultad de Ciencias, Universidad de Salamanca, Plaza de la Merced 1, 37008 Salamanca, Spain

DOI:

https://doi.org/10.33044/revuma.3192

Abstract

We determine generators of the coordinate ring of $\mathrm{SL}_2$-character varieties. In the case of the free group $F_3$ we obtain an explicit equation of the $\mathrm{SL}_2$-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 $\mathrm{SL}_2$-character variety and use the description to compute their $E$-polynomials.

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Published

2024-03-08

Issue

Vol. 67 No. 1 (2024)

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Article

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Copyright (c) 2024 Vicente Muñoz, Jesús Martín Ovejero

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