The scheme of characters in SL 2

Michael Heusener; Joan Porti

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arXiv · 2210.13888

The scheme of characters in SL 2

Michael Heusener·Joan Porti

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Abstract

The aim of this article is to study the SL(2,C)-character scheme of a finitely generated group. Given a presentation of a finitely generated group $\Gamma$, we give equations defining the coordinate ring of the scheme of SL(2,C)-characters of $\Gamma$ (finitely many equations when $\Gamma$ is finitely presented). We also study the scheme of abelian and nonsimple representations and characters. Finally we apply our results to study the SL(2,C)-character scheme of the Borromean rings.

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Michael Heusener, Joan Porti. 2022-10-25. The scheme of characters in SL 2. https://arxiv.org/abs/2210.13888

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