Quantum K-invariants and Gopakumar-Vafa invariants II. Calabi-Yau threefolds at genus zero
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915710097162240 |
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| author | Chou, You-Cheng Lee, Y. -P. |
| author_facet | Chou, You-Cheng Lee, Y. -P. |
| contents | This is the second part of our ongoing project on the relations between Gopakumar-Vafa BPS invariants (GV) and quantum K-theory (QK) on the Calabi--Yau threefolds (CY3). We show that on CY3 a genus zero quantum K-invariant can be written as a linear combination of a finite number of Gopakumar--Vafa invariants with coefficients from an explicit ``multiple cover formula''. Conversely, GV can be determined by QK in a similar manner. The technical heart is a proof of a remarkable conjecture by Hans Jockers and Peter Mayr.
This result is consistent with the ``virtual Clemens conjecture'' for the Calabi--Yau threefolds. A heuristic derivation of the relation between QK and GV via the virtual Clemens conjecture and the multiple cover formula is also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_08480 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum K-invariants and Gopakumar-Vafa invariants II. Calabi-Yau threefolds at genus zero Chou, You-Cheng Lee, Y. -P. Algebraic Geometry This is the second part of our ongoing project on the relations between Gopakumar-Vafa BPS invariants (GV) and quantum K-theory (QK) on the Calabi--Yau threefolds (CY3). We show that on CY3 a genus zero quantum K-invariant can be written as a linear combination of a finite number of Gopakumar--Vafa invariants with coefficients from an explicit ``multiple cover formula''. Conversely, GV can be determined by QK in a similar manner. The technical heart is a proof of a remarkable conjecture by Hans Jockers and Peter Mayr. This result is consistent with the ``virtual Clemens conjecture'' for the Calabi--Yau threefolds. A heuristic derivation of the relation between QK and GV via the virtual Clemens conjecture and the multiple cover formula is also given. |
| title | Quantum K-invariants and Gopakumar-Vafa invariants II. Calabi-Yau threefolds at genus zero |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2305.08480 |