论文标题
在奇异角色品种的杂货中多项式
On Hodge polynomials of Singular Character Varieties
论文作者
论文摘要
令$ \ mathcal {x}_γG：= \ mathrm {hom}（γ，g）/\！/g $为$ g $ -character的品种$γ$，其中$ g $是一个复杂的还原组，$γ$ $γ$是有限呈现的组。我们介绍了用于计算$ \ Mathcal {X}_γG$的Hodge-Deligne和serre多项式的新技术，并提出了一些应用程序，重点介绍了$γ$是免费或免费的Abelian群体的情况。主要结果的详细结构和主要结果证明将出现在其他地方。
Let $\mathcal{X}_ΓG:=\mathrm{Hom}(Γ,G)/\!/G$ be the $G$-character variety of $Γ$, where $G$ is a complex reductive group and $Γ$ a finitely presented group. We introduce new techniques for computing Hodge-Deligne and Serre polynomials of $\mathcal{X}_ΓG$, and present some applications, focusing on the cases when $Γ$ is a free or free abelian group. Detailed constructions and proofs of the main results will appear elsewhere.
