Cambridge Journal of Mathematics

Volume 4 (2016)

Number 3

Invariance of quantum rings under ordinary flops III: A quantum splitting principle

Pages: 333 – 401

DOI: https://dx.doi.org/10.4310/CJM.2016.v4.n3.a2

Authors

Yuan-Pin Lee (Department of Mathematics, University of Utah, Salt Lake City, Utah, U.S.A.)

Hui-Wen Lin (Department of Mathematics and Taida Institute of Mathematical Sciences (TIMS), National Taiwan University, Taipei, Taiwan)

Feng Qu (Beijing International Center for Mathematical Research, Beijing, China)

Chin-Lung Wang (Department of Mathematics and Taida Institute of Mathematical Sciences (TIMS), National Taiwan University, Taipei, Taiwan)

Abstract

In this paper we prove the invariance of quantum rings for general ordinary flops, whose local models are certain non-split toric bundles over arbitrary smooth bases. An essential ingredient in the proof is a quantum splitting principle which reduces a statement in Gromov–Witten theory on non-split bundles to the case of split bundles.

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Published 7 September 2016