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 $\mathcal{ M}_{ g,n}$.
Categories: math.AG