PreprintCC BY 4.0arXiv
Polynomial point counts for moduli spaces of curves with marked points
Abstract
We prove that the number of curves of a fixed genus g with n marked points over finite fields is a polynomial function of the cardinality of the field if and only if g = 0 or 3g + 2n is less than or equal to 24. This confirms a conjecture of Canning, Larson, and the authors.
Related
- Cetraro lectures on integrable systems and moduli spaces of curves
- On the Hodge and Tate conjectures for moduli spaces of curves
- A Murphy's law for supports of forgetful maps between moduli spaces of stable pointed curves
- Motivic Euler characteristics of moduli spaces of curves
- Finiteness of algebraic Weil-Petersson totally geodesic curves in pointed moduli spaces
BibTeX
@misc{payne2026polynomial,
title = {{Polynomial point counts for moduli spaces of curves with marked points}},
author = {Sam Payne and Thomas Willwacher},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06264},
eprint = {2609.06264},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06264},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Polynomial point counts for moduli spaces of curves with marked points
AU - Sam Payne
AU - Thomas Willwacher
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.06264
UR - https://arxiv.org/abs/2609.06264
AB - We prove that the number of curves of a fixed genus g with n marked points over finite fields is a polynomial function of the cardinality of the field if and only if g = 0 or 3g + 2n is less than or equal to 24. This confirms a conjecture of Canning, Larson, and the authors.
ER -