Volume 25, issue 2 (2021)

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The theory of $N$–mixed-spin-$P$ fields

Huai-Liang Chang, Shuai Guo, Jun Li and Wei-Ping Li

Geometry & Topology 25 (2021) 775–811

This is the first part of our project toward proving the Bershadsky–Cecotti–Ooguri–Vafa Feynman graph sum formula of all genera Gromov–Witten invariants of quintic Calabi–Yau threefolds. We introduce the notion of N–mixed-spin-P fields, construct their moduli spaces, their virtual cycles and their virtual localization formulas, and obtain a vanishing result associated with irregular graphs.

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Gromov–Witten, mirror symmetry, high genus, mixed-spin-$P$ fields, cosection localization
Mathematical Subject Classification 2010
Primary: 14D23, 14J33, 14N35
Received: 21 August 2019
Revised: 13 April 2020
Accepted: 20 May 2020
Published: 27 April 2021
Proposed: Jim Bryan
Seconded: Gang Tian, Dan Abramovich
Huai-Liang Chang
Department of Mathematics
Hong Kong University of Science and Technology
Clear Water Bay
Hong Kong
Shuai Guo
School of Mathematical Sciences and Beijing International Center for Mathematical Research
Peking University
Jun Li
Shanghai Center for Mathematical Sciences
Fudan University
Wei-Ping Li
Department of Mathematics
Hong Kong University of Science and Technology
Clear Water Bay
Hong Kong