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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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