PreprintCC BY 4.0arXiv
Motivic Euler characteristics of moduli spaces of curves
Abstract
A combination of recent results of Canning--Larson--Payne--Willwacher and Payne--Willwacher is that the motivic Euler characteristic of the moduli space Mg,n of nonsingular curves with n markings is polynomial in the Tate motive if and only if g=0 or 3g+2n<25. In the cases when g≥ 1 and 3g+2n<25, there are $32$ pairs (g,n) where the motivic Euler characteristic has been computed. We compute the motivic Euler characteristic for $9$ more pairs, leaving only $6$ pairs where the motivic Euler characteristic is polynomial but unknown. In genus $4$, we moreover compute the answer when n=7, i.e.~the first non-polynomial case.
Related
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BibTeX
@misc{bergstrom2026motivic,
title = {{Motivic Euler characteristics of moduli spaces of curves}},
author = {Jonas Bergström and Samir Canning and Dan Petersen and Johannes Schmitt},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09694},
eprint = {2610.09694},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09694},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Motivic Euler characteristics of moduli spaces of curves
AU - Jonas Bergström
AU - Samir Canning
AU - Dan Petersen
AU - Johannes Schmitt
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09694
UR - https://arxiv.org/abs/2610.09694
AB - A combination of recent results of Canning--Larson--Payne--Willwacher and Payne--Willwacher is that the motivic Euler characteristic of the moduli space M_g,n of nonsingular curves with n markings is polynomial in the Tate motive if and only if g=0 or 3g+2n<25. In the cases when g≥ 1 and 3g+2n<25, there are $32$ pairs (g,n) where the motivic Euler characteristic has been computed. We compute the motivic Euler characteristic for $9$ more pairs, leaving only $6$ pairs where the motivic Euler characteristic is polynomial but unknown. In genus $4$, we moreover compute the answer when n=7, i.e.~the first non-polynomial case.
ER -