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

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.

References in corpus (5)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• The Grothendieck group of algebraic stacks
• A geometric invariant of a finite group
• Counting Higgs bundles
• Moduli spaces, indecomposable objects and potentials over a finite field

Cited by in corpus (1)

• Lie algebroid connections, twisted Higgs bundles and motives of moduli spaces