Open Gromov–Witten Theory of K P 2 , K P 1 × P 1 , K W P 1 , 1 , 2 , K F 1 and Jacobi Forms

It was known through the efforts of many works that the generating functions in the closed Gromov–Witten theory of KP2 are meromorphic quasi-modular forms (Coates and Iritani in Kyoto J Math 58(4):695–864, 2018; Lho and Pandharipande in Adv Math 332:349–402, 2018; Coates and Iritani in Gromov–Witten...

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Veröffentlicht in:Communications in mathematical physics 2019-01, Vol.369 (2), p.675-719
Hauptverfasser: Bohan Fang, Ruan, Yongbin, Zhang, Yingchun, Zhou, Jie
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Sprache:eng
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Zusammenfassung:It was known through the efforts of many works that the generating functions in the closed Gromov–Witten theory of KP2 are meromorphic quasi-modular forms (Coates and Iritani in Kyoto J Math 58(4):695–864, 2018; Lho and Pandharipande in Adv Math 332:349–402, 2018; Coates and Iritani in Gromov–Witten invariants of local P2 and modular forms, arXiv:1804.03292 [math.AG], 2018) basing on the B-model predictions (Bershadsky et al. in Commun Math Phys 165:311–428, 1994; Aganagic et al. in Commun Math Phys 277:771–819, 2008; Alim et al. in Adv Theor Math Phys 18(2):401–467, 2014). In this article, we extend the modularity phenomenon to KP1×P1,KWP[1,1,2],KF1. More importantly, we generalize it to the generating functions in the open Gromov–Witten theory using the theory of Jacobi forms where the open Gromov–Witten parameters are transformed into elliptic variables.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-019-03440-5