Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 070, 49 pages      arXiv:1910.12348      https://doi.org/10.3842/SIGMA.2020.070
Contribution to the Special Issue on Integrability, Geometry, Moduli in honor of Motohico Mulase for his 65th birthday

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

Roman Fedorov a, Alexander Soibelman b and Yan Soibelman c
a)  University of Pittsburgh, Pittsburgh, PA, USA
b)  Aarhus University, Aarhus, Denmark
c)  Kansas State University, Manhattan, KS, USA

Received November 19, 2019, in final form July 10, 2020; Published online July 27, 2020

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.

Key words: parabolic Higgs bundles; parabolic bundles with connections; motivic classes; Donaldson-Thomas invariants; Macdonald polynomials.

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