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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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
29 October 2022
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| In: |
Advances in mathematics
Year: 2022, Volume: 408, Issue: B, Pages: 1-44 |
| ISSN: | 1090-2082 |
| DOI: | 10.1016/j.aim.2022.108605 |
| Online Access: | 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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| Author Notes: | Yalong Cao, Georg Oberdieck, Yukinobu Toda |
| Summary: | 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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| Item Description: | Gesehen am 12.12.2024 |
| Physical Description: | Online Resource |
| ISSN: | 1090-2082 |
| DOI: | 10.1016/j.aim.2022.108605 |