The Log Product Formula in Quantum K-theory

We prove a formula expressing the K-theoretic log Gromov-Witten invariants of a product of log smooth varieties $V \times W$ in terms of the invariants of V and W. The proof requires introducing log virtual fundamental classes in K-theory and verifying their various functorial properties. We introdu...

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Bibliographic Details
Published in:Mathematical proceedings of the Cambridge Philosophical Society 2023-09, Vol.175 (2), p.225-252
Main Authors: CHOU, YOU–CHENG, HERR, LEO, LEE, YUAN–PIN
Format: Article
Language:English
Subjects:
Algebra
Invariants
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Summary:We prove a formula expressing the K-theoretic log Gromov-Witten invariants of a product of log smooth varieties $V \times W$ in terms of the invariants of V and W. The proof requires introducing log virtual fundamental classes in K-theory and verifying their various functorial properties. We introduce a log version of K-theory and prove the formula there as well.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004123000063