Preprint
On compactifications of the SL(2,C) character varieties of punctured surfaces
ArXiv.org
05/20/2023
DOI: 10.48550/arxiv.2305.12306
Abstract
This paper addresses several conjectures and questions regarding the absolute and relative compactifications of the SL(2,C)-character variety of an n-punctured Riemann surface without boundary. We study a class of projective compactifications determined by ideal triangulations of the surface and prove explicit results concerning the boundary divisors of these compactifications. Notably, we establish that the boundary divisors are toric varieties and confirm a well-known conjecture asserting that the (dual) boundary complex of any (positive dimensional) relative character variety is a sphere. Additionally, we verify that relative SL(2,C)-character varieties are log Calabi-Yau. In a different vein, we enhance and streamline Komyo's compactification method, which utilizes a projective compactification of SL(2,C) to compactify the (relative) character varieties. Specifically, we construct a uniform relative compactification over the base space of Cn and determine its monodromy, addressing a question posed by Simpson.
Details
- Title: Subtitle
- On compactifications of the SL(2,C) character varieties of punctured surfaces
- Creators
- Mohammad Farajzadeh-TehraniCharles Frohman
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- DOI
- 10.48550/arxiv.2305.12306
- ISSN
- 2331-8422
- Language
- English
- Date posted
- 05/20/2023
- Academic Unit
- Mathematics
- Record Identifier
- 9984419358302771
Metrics
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