Equivariant Hodge polynomials of heavy/light moduli spaces

Abstract

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 ${\mathcal{M}}_{g,n}$.

21 pages, 3 tables. Edits based on referee suggestions