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

IF 0.5 4区数学 Q3 MATHEMATICS

Geometriae Dedicata Pub Date : 2023-11-23 DOI:10.1007/s10711-023-00867-y

Joseph Cummings, Christopher Manon

引用次数: 0

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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$$\textrm{SL}_2(\mathbb {C})$$自由群字符变化的Fano紧化

我们证明了$\textrm{SL}_2(\mathbb {C})$自由群特征变化$\mathcal {X}(F_g, \textrm{SL}_2(\mathbb {C}))$的一定紧化$\mathfrak {X}_g$是Fano。这种紧化已经由第二作者和Biswas、Lawton和Ramras分别研究过。这个结果的部分证明涉及到一个大族的整自反多面体的构造。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Geometriae Dedicata 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Geometriae Dedicata concentrates on geometry and its relationship to topology, group theory and the theory of dynamical systems. Geometriae Dedicata aims to be a vehicle for excellent publications in geometry and related areas. Features of the journal will include: A fast turn-around time for articles. Special issues centered on specific topics. All submitted papers should include some explanation of the context of the main results. Geometriae Dedicata was founded in 1972 on the initiative of Hans Freudenthal in Utrecht, the Netherlands, who viewed geometry as a method rather than as a field. The present Board of Editors tries to continue in this spirit. The steady growth of the journal since its foundation is witness to the validity of the founder''s vision and to the success of the Editors'' mission.