Counting points on generic character varieties
Algebraic Geometry
2026-01-23 v4 Representation Theory
Abstract
We count points on character varieties associated with punctured surfaces and regular semisimple generic conjugacy classes in reductive groups. We find that the number of points are palindromic polynomials. This suggests a conjecture for these varieties. We also count points on the corresponding additive character varieties and find that the number of points are also polynomials, which we conjecture have non-negative coefficients. These polynomials can be considered as the reductive analogues of the Kac polynomials of comet-shaped quivers.
Cite
@article{arxiv.2409.04735,
title = {Counting points on generic character varieties},
author = {Masoud Kamgarpour and GyeongHyeon Nam and Bailey Whitbread and Stefano Giannini},
journal= {arXiv preprint arXiv:2409.04735},
year = {2026}
}
Comments
Final Version. To appear in Mathematics Research Letters. Updated references