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 |
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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. |
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ISSN: | 0010-3616 1432-0916 |
DOI: | 10.1007/s00220-019-03440-5 |