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arXiv · 2209.02766

A Fano compactification of the $\mathrm{SL}_2(\mathbb{C})$ free group character variety

Joseph Cummings·Christopher Manon
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Abstract

We show that a certain compactification $\mathfrak{X}_g$ of the $\mathrm{SL}_2(\mathbb{C})$ free group character variety $\mathcal{X}(F_g, \mathrm{SL}_2(\mathbb{C}))$ is Fano. This compactification has been studied previously by the second author, and separately by Biswas, Lawton, and Ramras. Part of the proof of this result involves the construction of a large family of integral reflexive polytopes.

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Joseph Cummings, Christopher Manon. 2022-09-06. A Fano compactification of the $\mathrm{SL}_2(\mathbb{C})$ free group character variety. https://arxiv.org/abs/2209.02766

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