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The Log Product Formula in Quantum K-theory

Part of: Cycles and subschemes Projective and enumerative geometry

Published online by Cambridge University Press:  11 April 2023

YOU–CHENG CHOU ,
LEO HERR  and
YUAN–PIN LEE
YOU–CHENG CHOU
Affiliation:
Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan and Department of Mathematics, University of Utah, Salt Lake City, Utah 84112-0090, U.S.A. e-mails: chou@math.utah.edu, herr@math.utah.edu, yplee@math.utah.edu
LEO HERR
Affiliation:
Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan and Department of Mathematics, University of Utah, Salt Lake City, Utah 84112-0090, U.S.A. e-mails: chou@math.utah.edu, herr@math.utah.edu, yplee@math.utah.edu
YUAN–PIN LEE
Affiliation:
Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan and Department of Mathematics, University of Utah, Salt Lake City, Utah 84112-0090, U.S.A. e-mails: chou@math.utah.edu, herr@math.utah.edu, yplee@math.utah.edu
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Abstract

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.

MSC classification

Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants
Secondary: 14C35: Applications of methods of algebraic $K$-theory
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 175 , Issue 2 , September 2023 , pp. 225 - 252
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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