Motivic Donaldson-Thomas Invariants of Parabolic Higgs Bundles and Parabolic Connections on a Curve
Let be a smooth projective curve over a field of characteristic zero, and let be a non-empty set of rational points of . We calculate the motivic classes of moduli stacks of semistable parabolic bundles with connections on (, ) and the motivic classes of moduli stacks of semistable parabolic Higgs...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210778 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Motivic 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 |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862683803828355072 |
|---|---|
| author | Fedorov, Roman Soibelman, Alexander Soibelman, Yan |
| author_facet | Fedorov, Roman Soibelman, Alexander Soibelman, Yan |
| citation_txt | Motivic 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 |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Let be a smooth projective curve over a field of characteristic zero, and let be a non-empty set of rational points of . We calculate the motivic classes of moduli stacks of semistable parabolic bundles with connections on (, ) and the motivic classes of moduli stacks of semistable parabolic Higgs bundles on (, ). 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.
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| first_indexed | 2026-03-17T09:13:25Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210778 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-17T09:13:25Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Fedorov, Roman Soibelman, Alexander Soibelman, Yan 2025-12-17T14:37:10Z 2020 Motivic 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 1815-0659 2020 Mathematics Subject Classification: 14D23; 14N35; 14D20 arXiv:1910.12348 https://nasplib.isofts.kiev.ua/handle/123456789/210778 https://doi.org/10.3842/SIGMA.2020.070 Let be a smooth projective curve over a field of characteristic zero, and let be a non-empty set of rational points of . We calculate the motivic classes of moduli stacks of semistable parabolic bundles with connections on (, ) and the motivic classes of moduli stacks of semistable parabolic Higgs bundles on (, ). 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. We 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Motivic Donaldson-Thomas Invariants of Parabolic Higgs Bundles and Parabolic Connections on a Curve Article published earlier |
| spellingShingle | Motivic Donaldson-Thomas Invariants of Parabolic Higgs Bundles and Parabolic Connections on a Curve Fedorov, Roman Soibelman, Alexander Soibelman, Yan |
| title | Motivic Donaldson-Thomas Invariants of Parabolic Higgs Bundles and Parabolic Connections on a Curve |
| title_full | Motivic Donaldson-Thomas Invariants of Parabolic Higgs Bundles and Parabolic Connections on a Curve |
| title_fullStr | Motivic Donaldson-Thomas Invariants of Parabolic Higgs Bundles and Parabolic Connections on a Curve |
| title_full_unstemmed | Motivic Donaldson-Thomas Invariants of Parabolic Higgs Bundles and Parabolic Connections on a Curve |
| title_short | Motivic Donaldson-Thomas Invariants of Parabolic Higgs Bundles and Parabolic Connections on a Curve |
| title_sort | motivic donaldson-thomas invariants of parabolic higgs bundles and parabolic connections on a curve |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210778 |
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