Singularities of character varieties

Cheng Shu

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arXiv · 2412.03436

Singularities of character varieties

Cheng Shu

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Abstract

For any complex reductive group $G$ and any compact Riemann surface with genus $g>0$, we show that every connected component of the associated character variety is $\mathbb{Q}$-factorial and has symplectic singularities, and classify the connected components that admit symplectic resolutions. When $g>1$, we use elliptic endoscopic groups to control the singularities caused by irreducible local systems with automorphism groups larger than the centre of $G$; when $g=1$, our analysis is based on some results of Borel-Friedman-Morgan. The main results for $g>1$ were obtained by Herbig-Schwarz-Seaton via a different approach.

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Cheng Shu. 2024-12-04. Singularities of character varieties. https://arxiv.org/abs/2412.03436

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