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

Abstract

We show that a certain compactification \(\mathfrak {X}_g\) of the \(\textrm{SL}_2(\mathbb {C})\) free group character variety \(\mathcal {X}(F_g, \textrm{SL}_2(\mathbb {C}))\) 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.