Equivariant Hodge polynomials of heavy/light moduli spaces

Abstract

Let $\overline {\mathcal {M}}_{g, m|n}$ denote Hassett’s moduli space of weighted pointed stable curves of genus g for the heavy/light weight data $$\begin{align*}\left(1^{(m)}, 1/n^{(n)}\right),\end{align*}$$

and let $\mathcal {M}_{g, m|n} \subset \overline {\mathcal {M}}_{g, m|n}$ 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 $\overline {\mathcal {M}}_{g,n}$ and $\mathcal {M}_{g,n}$.