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

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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.

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  1. B21 Hayes-Healy Center, 100, Notre Dame, IN, 46556, USA

    Joseph Cummings

  2. 959 Patterson Office Tower,120 Patterson Dr, Lexington, KY, 40506, USA

    Christopher Manon

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  1. Joseph Cummings
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Cummings, J., Manon, C. A Fano compactification of the \(\textrm{SL}_2(\mathbb {C})\) free group character variety. Geom Dedicata 218, 17 (2024). https://doi.org/10.1007/s10711-023-00867-y

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