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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 studiedpreviously 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 ofintegral reflexive polytopes.

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