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

Joseph Cummings; Christopher Manon

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

Algebraic Geometry 2022-09-08 v1

Authors: Joseph Cummings , Christopher Manon

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.

Keywords

fano compactification character variety free group sl2(c) reflexive polytope

Cite

@article{arxiv.2209.02766,
  title  = {A Fano compactification of the $\mathrm{SL}_2(\mathbb{C})$ free group character variety},
  author = {Joseph Cummings and Christopher Manon},
  journal= {arXiv preprint arXiv:2209.02766},
  year   = {2022}
}

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16 pages, 5 figures

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

Abstract

Keywords

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