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arXiv · 2202.07227

Coordinate rings of some $SL_2$-character varieties

Vicente Muñoz·Jesús Martín Ovejero
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Abstract

We determine generators of the coordinate ring of $SL_2$-character varieties. In the case of the free group $F_3$ we obtain an explicit equation of the $SL_2$-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 $SL_2$-character variety and use the description to compute their E-polynomials.

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Vicente Muñoz, Jesús Martín Ovejero. 2022-02-15. Coordinate rings of some $SL_2$-character varieties. https://arxiv.org/abs/2202.07227

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