Year: 2026
Type: preprint
Abstract: By studying wall crossings of Hassett moduli spaces of weighted pointed curves, we prove a recursive formula that reduces the computation of the cohomology of $\overline{\mathcal M}_{g,n}$ to that of the moduli space $\overline{\mathcal M}_{g,(0^+)^n}$ of stable pointed curves of minimal weights. For $g=1$, we further prove an explicit formula for the Hodge-Deligne and Poincaré polynomials of $\overline{\mathcal M}_{1,(0^+)^n}$. Combining these, we prove formulas that enable us to compute the cohomology of $\overline{\mathcal M}_{1,n}$ efficiently.
Source: arXiv (Cornell University)
Author: Kiem, Young-Hoon
Institution: Korea Institute for Advanced Study
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212586840