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arXiv · 1010.5287

Open Gromov-Witten invariants and superpotentials for semi-Fano toric surfaces

Kwokwai Chan·Siu-Cheong Lau
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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 non-trivial 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.

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Kwokwai Chan, Siu-Cheong Lau. 2013-03-27. Open Gromov-Witten invariants and superpotentials for semi-Fano toric surfaces. https://doi.org/10.1093/imrn%2Frnt050

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