Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds
As an analogy to Gopakumar-Vafa conjecture on Calabi-Yau 3-folds, Klemm-Pandharipande defined Gopakumar-Vafa type invariants of a Calabi-Yau 4-fold X using Gromov-Witten theory. When X is holomorphic symplectic, Gromov-Witten invariants vanish and one can consider the corresponding reduced theory. I...
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| Hauptverfasser: | , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
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29 October 2022
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| In: |
Advances in mathematics
Year: 2022, Jahrgang: 408, Heft: B, Pages: 1-44 |
| ISSN: | 1090-2082 |
| DOI: | 10.1016/j.aim.2022.108605 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.aim.2022.108605 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0001870822004224 
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| Verfasserangaben: | Yalong Cao, Georg Oberdieck, Yukinobu Toda |
MARC
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| 520 | |a As an analogy to Gopakumar-Vafa conjecture on Calabi-Yau 3-folds, Klemm-Pandharipande defined Gopakumar-Vafa type invariants of a Calabi-Yau 4-fold X using Gromov-Witten theory. When X is holomorphic symplectic, Gromov-Witten invariants vanish and one can consider the corresponding reduced theory. In a companion work, we propose a definition of Gopakumar-Vafa type invariants for such a reduced theory. In this paper, we give them a sheaf theoretic interpretation via moduli spaces of stable pairs. | ||
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