E-polynomials of character varieties for real curves

2020/06/01 by Thomas John Baird, Baird, Thomas John, Michael Lennox Wong +1
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.2006.01288

Abstract

We calculate the E-polynomial for a class of the (complex) character varieties M_n^τ associated to a genus g Riemann surface Σ equipped with an orientation reversing involution τ. Our formula expresses the generating function ∑_n=1^∞ E(M_n^τ) Tⁿ as the plethystic logarithm of a product of sums indexed by Young diagrams. The proof uses point counting over finite fields, emulating Hausel and Rodriguez-Villegas.

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