Coordinate ring of $\mathrm{SL}_2$-character varieties.

• Vicente Muñoz ^[1] ; Jesús Martín Ovejero ^[2]
  1. [1] Universidad de Málaga

     Universidad de Málaga

     Málaga, España

     
  2. [2] Universidad de Salamanca

     Universidad de Salamanca

     Salamanca, España

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 67, Nº. 1, 2024, págs. 47-64
• Idioma: inglés
• Enlaces
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• Resumen

  • We determine generators of the coordinate ring of SL2-character varieties. In the case of the free group F3 we obtain an explicit equation of the SL2-character variety. For free groups Fk, we find transcendental generators. Finally, for the case of the 2-torus, we get an explicit equation of the SL2-character variety and use the description to compute their E-polynomials.