Mixed Hodge polynomials of character varieties
Mixed Hodge polynomials of character varieties
复制标题
性状变异的混合Hodge多项式
DOI：
10.1007/s00222-008-0142-x
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发表时间：
2006
影响因子：
3.1
通讯作者：
F. Rodriguez
中科院分区：
文献类型：
--
作者：
Tamás Hausel;F. Rodriguez
本文利用有限Lie型群的特征标表和附录中N.卡茨我们从这个计算中推导出几个几何结果，例如，相关的PGL（n，n）-特征标簇的拓扑欧拉特征的值。计算还导致了几个关于$\mathcal {M}_{n}$上同调的猜想：一个明确的猜想其混合霍奇多项式;一个明确的好奇硬莱夫谢茨定理和一个猜想有关的纯部分绝对不可分解的表示一定的矩阵。我们证明了n = 2时的这些定理。
We calculate the E-polynomials of certain twisted GL(n,ℂ)-character varieties $\mathcal{M}_{n}$ of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type $\text{GL}(n,\mathbb{F}_{q})$ and a theorem proved in the appendix by N. Katz. We deduce from this calculation several geometric results, for example, the value of the topological Euler characteristic of the associated PGL(n,ℂ)-character variety. The calculation also leads to several conjectures about the cohomology of $\mathcal{M}_{n}$: an explicit conjecture for its mixed Hodge polynomial; a conjectured curious hard Lefschetz theorem and a conjecture relating the pure part to absolutely indecomposable representations of a certain quiver. We prove these conjectures for n=2.