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arXiv · 2305.08480

Quantum K-invariants and Gopakumar-Vafa invariants II. Calabi-Yau threefolds at genus zero

You-Cheng Chou·Y. -P. Lee
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Abstract

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.

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You-Cheng Chou, Y. -P. Lee. 2023-05-15. Quantum K-invariants and Gopakumar-Vafa invariants II. Calabi-Yau threefolds at genus zero. https://doi.org/10.2140/gt.2025.29.4665

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