标题： 特征簇的奇点 显示英文标题

标题： Singularities of character varieties

摘要： 对于任意的复约化群 $G$ 和任意具有亏格 $g>0$ 的紧致黎曼面，我们证明了与之相关的特征簇的每个连通分支都是 $\mathbb{Q}$-因子化，并且具有辛奇点，同时分类了允许辛分解的连通分支。 当 $g>1$ 时，我们利用椭圆端几何群来控制由自同构群比 $G$ 的中心更大的不可约局部系统引起的奇点；当 $g=1$ 时，我们的分析基于 Borel-Friedman-Morgan 的一些结果。 对于 $g>1$，Herbig-Schwarz-Seaton 通过不同的方法得到了主要结果。 显示英文摘要

摘要： 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.