论文标题
真实曲线的角色品种的电子多项式
E-polynomials of character varieties for real curves
论文作者
论文摘要
我们计算了（复杂）字符品种$ \ mathcal {m} _n^τ$与属$ g $ g $ g $ riemann surface $σ$相关的（复杂）字符品种的e-polynomial。我们的公式表示生成函数$ \ sum_ {n = 1}^{\ infty} e（\ Mathcal {m} _n^τ）t^n $，是由年轻图索引的总和的多数对数。该证明使用对有限场，模拟Hausel和Rodriguez-Villegas的点进行计数。
We calculate the E-polynomial for a class of the (complex) character varieties $\mathcal{M}_n^τ$ associated to a genus $g$ Riemann surface $Σ$ equipped with an orientation reversing involution $τ$. Our formula expresses the generating function $\sum_{n=1}^{\infty} E(\mathcal{M}_n^τ) T^n$ as the plethystic logarithm of a product of sums indexed by Young diagrams. The proof uses point counting over finite fields, emulating Hausel and Rodriguez-Villegas.
