PreprintCC BY 4.0arXiv
Hodge-Deligne and Poincaré polynomials of ℳ̅1,n
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 ℳ̅g,n to that of the moduli space ℳ̅g,(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 ℳ̅1,(0+)n. Combining these, we prove formulas that enable us to compute the cohomology of ℳ̅1,n efficiently.
Related
- Hodge--Deligne polynomials and Sn-representations on the cohomology of ℳ̅2,n
- Compactification Independence of the Irregular Hodge Filtration on Deligne-Mumford Stacks
- Irregular Hodge Bundles for Deligne--Mumford Landau--Ginzburg Families with Fixed Pole Orders
- Palindromic Poincaré polynomials in Bn
- Poincare Polynomials of Heavy-Light Hassett Spaces
BibTeX
@misc{kiem2026hodgedeligne,
title = {{Hodge-Deligne and Poincaré polynomials of $\overline\mathcal M_1,n$}},
author = {Young-Hoon Kiem},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.12507},
eprint = {2609.12507},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12507},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hodge-Deligne and Poincaré polynomials of ℳ̅_1,n
AU - Young-Hoon Kiem
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2609.12507
UR - https://arxiv.org/abs/2609.12507
AB - 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 ℳ̅_g,n to that of the moduli space ℳ̅_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 ℳ̅_1,(0^+)^n. Combining these, we prove formulas that enable us to compute the cohomology of ℳ̅_1,n efficiently.
ER -