论文标题
重型/轻型模量空间的霍奇多项式
Equivariant Hodge polynomials of heavy/light moduli spaces
论文作者
论文摘要
令$ \ bar {\ Mathcal {m}} _ {g，m | n} $表示Hassett的Moduli的Moduli，重量/轻度数据$ \ left（1^{（M）}，1/N^{（N）}} $ g $ g $ g $ g $ g $ g $的稳定曲线，并将m | n} \ subset \ bar {\ mathcal {m}} _ {g，m | n} $是参数化的基因座，不一定明显标记为曲线。我们给出了一个变化的公式，该公式可以根据$ s_ {n} $ - equivariant-equivariant Hodge-deligne polynomials的生成函数来计算这些空间的$（s_m \ times s_n）$ - equivariant equivariant equivariant hodge-deligne多项式的$ __和$ \ mathcal {m} _ {g，n} $。
Let $\bar{\mathcal{M}}_{g, m|n}$ denote Hassett's moduli space of weighted pointed stable curves of genus $g$ for the heavy/light weight data $\left(1^{(m)}, 1/n^{(n)}\right)$, and let $\mathcal{M}_{g, m|n} \subset \bar{\mathcal{M}}_{g, m|n}$ be the locus parameterizing smooth, not necessarily distinctly marked curves. We give a change-of-variables formula which computes the generating function for $(S_m\times S_n)$-equivariant Hodge-Deligne polynomials of these spaces in terms of the generating functions for $S_{n}$-equivariant Hodge-Deligne polynomials of $\bar{\mathcal{M}}_{g,n}$ and $\mathcal{M}_{g,n}$.
