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Quantum $K$-invariants
and Gopakumar–Vafa invarints, II: Calabi–Yau threefolds at
genus zero
You-Cheng Chou and Yuan-Pin Lee |
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Geometry & Topology 29 (2025) 4665–4693
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DOI: 10.2140/gt.2025.29.4665
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Abstract |
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This is the second part of our ongoing project on the relations between Gopakumar–Vafa BPS invariants (GV) and quantum -theory (QK) on the Calabi–Yau threefolds (CY3). We show that on CY3, a genus-zero quantum -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. |
Keywords
quantum $K$-theory, Gopakumar–Vafa invariant
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Mathematical Subject Classification
Primary: 14N35, 53D45
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References |
Publication
Received: 12 August 2023
Revised: 17 July 2024
Accepted: 22 March 2025
Published: 31 December 2025
Proposed: Jim Bryan
Seconded: Dan Abramovich, Arend Bayer
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Authors |
| You-Cheng Chou | |
| Institute of Mathematics Academia Sinica Taipei Taiwan |
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| Yuan-Pin Lee | |
| Institute Of Mathematics Academia Sinica Taipei Taiwan |
Department of Mathematics University of Utah Salt Lake City, UT United States |
| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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