Solutions of the motivic ADHM recursion formula

TL;DR

This paper provides explicit solutions to the motivic ADHM recursion formula, linking it to Hodge polynomials of Higgs moduli spaces and proposing a conjectural formula for motives of twisted Higgs moduli spaces.

Contribution

It offers the first explicit solutions to the motivic ADHM recursion formula and extends conjectures relating motives of Higgs moduli spaces.

Findings

Explicit solution to the ADHM recursion formula

Connection to Hodge polynomials of Higgs moduli spaces

Conjectural formula for motives of twisted Higgs moduli spaces

Abstract

We give an explicit solution of the ADHM recursion formula conjectured by Chuang, Diaconescu, and Pan. This solution is closely related to the formula for the Hodge polynomials of Higgs moduli spaces conjectured by Hausel and Rodriguez-Villegas. We solve also the twisted motivic ADHM recursion formula. As a byproduct we obtain a conjectural formula for the motives of twisted Higgs moduli spaces, which generalizes the conjecture of Hausel and Rodriguez-Villegas.