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

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dc.contributor.authorFedorov, Roman
dc.contributor.authorSoibelman, Alexander
dc.contributor.authorSoibelman, Yan
dc.date.accessioned2025-12-17T14:37:10Z
dc.date.issued2020
dc.description.abstractLet 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.
dc.description.sponsorshipWe thank E. Diaconescu, J. Heinloth, O. Schi mann, and especially A. Mellit for useful discussions and correspondence. We thank P. Boalch for a useful comment on an earlier version. A part of this work was done while R.F. was visiting the Max Planck Institute of Mathematics in Bonn, and a part when he was visiting A. Mellit at the University of Vienna. The work of R.F. was partially supported by NSF grant DMS1406532. A.S. and Y.S. thank IHES for excellent research conditions and hospitality. The work of Y.S. was partially supported by NSF grants and the Munson-Simu Faculty Award at Kansas State University. The authors would like to thank the anonymous referees for carefully reading the paper and for their useful comments.
dc.identifier.citationMotivic Donaldson-Thomas Invariants of Parabolic Higgs Bundles and Parabolic Connections on a Curve. Roman Fedorov, Alexander Soibelman and Yan Soibelman. SIGMA 16 (2020), 070, 49 pages
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2020.070
dc.identifier.issn1815-0659
dc.identifier.other2020 Mathematics Subject Classification: 14D23; 14N35; 14D20
dc.identifier.otherarXiv:1910.12348
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/210778
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleMotivic Donaldson-Thomas Invariants of Parabolic Higgs Bundles and Parabolic Connections on a Curve
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2020, том 16, випуск за цей рік