Motivic Donaldson-Thomas Invariants of Parabolic Higgs Bundles and Parabolic Connections on a Curve

TL;DR

This paper computes motivic classes of moduli stacks of semistable parabolic bundles with connections and Higgs bundles on a curve, providing criteria for their non-emptiness related to the Deligne-Simpson problem.

Contribution

It introduces explicit calculations of motivic classes for these moduli stacks and establishes non-emptiness criteria, advancing understanding of parabolic Higgs bundles and connections.

Findings

Motivic classes of moduli stacks are explicitly calculated.

Non-emptiness criteria for these stacks are established.

Results relate to the Deligne-Simpson problem.

Abstract

Let $X$ be a smooth projective curve over a field of characteristic zero and let $D$ be a non-empty set of rational points of $X$. We calculate the motivic classes of moduli stacks of semistable parabolic bundles with connections on $(X,D)$ and motivic classes of moduli stacks of semistable parabolic Higgs bundles on $(X,D)$. As a by-product we give a criteria for non-emptiness of these moduli stacks, which can be viewed as a version of the Deligne-Simpson problem.