Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Payne, Sam, Willwacher, Thomas
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212084356