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

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.

16 pages, 5 figures