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

Abstract

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