Genus zero Gopakumar–Vafa type invariants for Calabi–Yau 4-folds
© 2018 Elsevier Inc. In analogy with the Gopakumar–Vafa conjecture on CY 3-folds, Klemm and Pandharipande defined GV type invariants on Calabi–Yau 4-folds using Gromov–Witten theory and conjectured their integrality. In this paper, we propose a sheaf-theoretic interpretation of their genus zero inva...
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| Format: | Article |
| Language: | English |
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Elsevier BV
2021
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| Online Access: | https://hdl.handle.net/1721.1/136350 |
| _version_ | 1826215164747186176 |
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| author | Cao, Yalong Maulik, Davesh Toda, Yukinobu |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Cao, Yalong Maulik, Davesh Toda, Yukinobu |
| author_sort | Cao, Yalong |
| collection | MIT |
| description | © 2018 Elsevier Inc. In analogy with the Gopakumar–Vafa conjecture on CY 3-folds, Klemm and Pandharipande defined GV type invariants on Calabi–Yau 4-folds using Gromov–Witten theory and conjectured their integrality. In this paper, we propose a sheaf-theoretic interpretation of their genus zero invariants using Donaldson–Thomas theory on CY 4-folds. More specifically, we conjecture genus zero GV type invariants are DT4 invariants for one-dimensional stable sheaves on CY 4-folds. Some examples are computed for both compact and non-compact CY 4-folds to support our conjectures. We also propose an equivariant version of the conjectures for local curves and verify them in certain cases. |
| first_indexed | 2024-09-23T16:17:36Z |
| format | Article |
| id | mit-1721.1/136350 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:17:36Z |
| publishDate | 2021 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1363502023-12-20T15:50:48Z Genus zero Gopakumar–Vafa type invariants for Calabi–Yau 4-folds Cao, Yalong Maulik, Davesh Toda, Yukinobu Massachusetts Institute of Technology. Department of Mathematics © 2018 Elsevier Inc. In analogy with the Gopakumar–Vafa conjecture on CY 3-folds, Klemm and Pandharipande defined GV type invariants on Calabi–Yau 4-folds using Gromov–Witten theory and conjectured their integrality. In this paper, we propose a sheaf-theoretic interpretation of their genus zero invariants using Donaldson–Thomas theory on CY 4-folds. More specifically, we conjecture genus zero GV type invariants are DT4 invariants for one-dimensional stable sheaves on CY 4-folds. Some examples are computed for both compact and non-compact CY 4-folds to support our conjectures. We also propose an equivariant version of the conjectures for local curves and verify them in certain cases. 2021-10-27T20:34:59Z 2021-10-27T20:34:59Z 2018 2019-11-14T19:40:21Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/136350 en 10.1016/J.AIM.2018.08.013 Advances in Mathematics Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier BV arXiv |
| spellingShingle | Cao, Yalong Maulik, Davesh Toda, Yukinobu Genus zero Gopakumar–Vafa type invariants for Calabi–Yau 4-folds |
| title | Genus zero Gopakumar–Vafa type invariants for Calabi–Yau 4-folds |
| title_full | Genus zero Gopakumar–Vafa type invariants for Calabi–Yau 4-folds |
| title_fullStr | Genus zero Gopakumar–Vafa type invariants for Calabi–Yau 4-folds |
| title_full_unstemmed | Genus zero Gopakumar–Vafa type invariants for Calabi–Yau 4-folds |
| title_short | Genus zero Gopakumar–Vafa type invariants for Calabi–Yau 4-folds |
| title_sort | genus zero gopakumar vafa type invariants for calabi yau 4 folds |
| url | https://hdl.handle.net/1721.1/136350 |
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