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arXiv · 2609.12507

Hodge-Deligne and Poincaré polynomials of $\overline{\mathcal M}_{1,n}$

Young-Hoon Kiem
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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.

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Young-Hoon Kiem. 2026-09-11. Hodge-Deligne and Poincaré polynomials of $\overline{\mathcal M}_{1,n}$. https://arxiv.org/abs/2609.12507

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