Counting stringy points on a family of character varieties

2024/11/08 by Lucas de Amorin, de Amorin, Lucas, Martı́n Mereb +1
Computer Science · #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #Data Management and Algorithms #FOS: Mathematics #Polynomial and algebraic computation #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2411.05563

openalex publication_date 2024/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provided explicit formulas for the number of stringy points over finite fields of parabolic type A character varieties with generic semisimple monodromy. This leads to formulas for their stringy E-polynomials. In particular, they satisfy the Betti Topological Mirror Symmetry Conjecture of T. Hausel and M. Thaddeus, as well as a refinement regarding isotypic components. Our proof is based on a Frobenius' type formula for Clifford's type settings and an analysis of it in a specific set-up related to regular wreath products with cyclic groups.

Related

• E-polynomials of character varieties for real curves
• Counting points on generic character varieties
• On the E-polynomials of a family of Character Varieties
• On the E-polynomial of parabolic Sp_2n-character varieties
• Arithmetic geometry of character varieties with regular monodromy