Semantic Scholar Open Access 2018 6 sitasi

Open Gromov–Witten Theory of $$K_{{\mathbb {P}}^2}, K_{{{\mathbb {P}}^1}\times {{\mathbb {P}}^1}}, K_{W{\mathbb {P}}\left[ 1,1,2\right] }, K_{{{\mathbb {F}}}_1}$$KP2,KP1×P1,KWP1,1,2,KF1 and Jacobi Forms

Bohan Fang Y. Ruan Yingchun Zhang Jie Zhou

Lihat Sumber DOI

Abstrak

It was known through the efforts of many works that the generating functions in the closed Gromov–Witten theory of $$K_{{\mathbb {P}}^2}$$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 $${\mathbb {P}}^{2}$$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 $$K_{{{\mathbb {P}}^1}\times {{\mathbb {P}}^1}}, K_{W{\mathbb {P}}[1,1,2]}, K_{{\mathbb {F}}_1}$$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.

Topik & Kata Kunci

Mathematics Physics

Penulis (4)

Bohan Fang

Y. Ruan

Yingchun Zhang

Jie Zhou

Format Sitasi

APA MLA BibTeX

Fang, B., Ruan, Y., Zhang, Y., Zhou, J. (2018). Open Gromov–Witten Theory of $$K_{{\mathbb {P}}^2}, K_{{{\mathbb {P}}^1}\times {{\mathbb {P}}^1}}, K_{W{\mathbb {P}}\left[ 1,1,2\right] }, K_{{{\mathbb {F}}}_1}$$KP2,KP1×P1,KWP1,1,2,KF1 and Jacobi Forms. https://doi.org/10.1007/s00220-019-03440-5

Akses Cepat

Lihat di Sumber doi.org/10.1007/s00220-019-03440-5

Informasi Jurnal

Tahun Terbit: 2018
Bahasa: en
Total Sitasi: 6×
Sumber Database: Semantic Scholar
DOI: 10.1007/s00220-019-03440-5
Akses: Open Access ✓