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- Title
Open Gromov–Witten Invariants and Superpotentials for Semi-Fano Toric Surfaces.
- Authors
Chan, Kwokwai; Lau, Siu-Cheong
- Abstract
In this paper, we compute the open Gromov–Witten invariants for every compact toric surface X which is semi-Fano (i.e., the anticanonical line bundle is nef). Unlike the Fano case, this involves nontrivial obstructions in the corresponding moduli problem. As a consequence, an explicit formula for the Lagrangian Floer superpotential W is obtained, which in turn gives an explicit presentation of the small quantum cohomology ring of X. We also provide a computational verification of the conjectural ring isomorphism between the small quantum cohomology of X and the Jacobian ring of W.
- Subjects
GROMOV-Witten invariants; INVARIANTS (Mathematics); JACOBIAN determinants; COHOMOLOGY theory; MODULI theory
- Publication
IMRN: International Mathematics Research Notices, 2014, Vol 2014, Issue 14, p3759
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnt050