A Super Version of a Theorem of Fricke-Klein
Algebraic Geometry
2026-03-24 v3
Abstract
We start studying the character variety of the algebraic supergroup OSp(1|2) from the algebraic perspective. We do this by first investigating the specific case of the character variety of the free group on two letters and try to describe the ring of invariants with respect to the conjugation action. The explicit description of the corresponding character variety for SL(2) was done by Fricke and Klein, so this can be seen as a variant of this theorem for its supergeometric counterpart OSp(1|2) and briefly touch upon the character stack for OSp(1|2)
Cite
@article{arxiv.2602.20482,
title = {A Super Version of a Theorem of Fricke-Klein},
author = {Marcel Dang},
journal= {arXiv preprint arXiv:2602.20482},
year = {2026}
}
Comments
31 pages, comments welcome. (v3) added an example after the main theorem and some comments,(v2) reorganized the material, corrected typos, added a section about character stacks