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On weighted-blowup formulae of genus zero orbifold Gromov–Witten invariants

Part of: Projective and enumerative geometry Symplectic geometry, contact geometry

Published online by Cambridge University Press:  19 July 2023

Bohui Chen  and
Cheng-Yong Du
Bohui Chen
Affiliation:
Department of Mathematics, Sichuan University, Chengdu 610065, China [email protected]
Cheng-Yong Du
Affiliation:
School of Mathematical Science, V. C. & V. R. Key Lab, and Laurent Mathematics Center, Sichuan Normal University, Chengdu 610068, China [email protected]
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Abstract

In this paper, we provide a new approach to prove some weighted-blowup formulae for genus zero orbifold Gromov–Witten invariants. As a consequence, we show the invariance of symplectically rational connectedness with respect to weighted-blowup along positive centers. Furthermore, we use this method to give a new proof to the genus zero relative-orbifold correspondence of Gromov–Witten invariants.

Keywords

Gromov–Witten invariantsweighted-blowup formulaesymplectically rational connectednesssymplectic unirulednessrelative-orbifold correspondence

MSC classification

Primary: 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
Secondary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants
Type
Research Article
Information
Compositio Mathematica , Volume 159 , Issue 9 , September 2023 , pp. 1833 - 1871
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Copyright
© 2023 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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Footnotes

This work was supported by the National Natural Science Foundation of China (No. 11890663, No. 12071322, No. 11826102, No. 11890660), by the National Key R&D Program of China (No. 2020YFA0714000), by Sichuan Science and Technology Program (No. 2022JDTD0019), and by Sichuan University, China (No. 1082204112190).

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