# Department of Mathematics

## Motivic Donaldson-Thomas invariants of parabolic Higgs bundles and parabolic connections on a curve

Research output: Working paperResearch

• Roman Fedorov, University of Pittsburgh
• ,
• Alexander Soibelman
• Yan Soibelman, Kansas State University
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 when these moduli stacks are non-empty, which can be viewed as a version of Deligne-Simpson problem.
Original language English ArXiv Published - Oct 2019

39 pages

### Research areas

• math.AG, hep-th, math-ph, math.KT, math.MP, math.SG

Citationformats

ID: 179377508