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

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

2010-10-25

arxiv.org/abs/1010.5287v1

Mathematics

Algebraic Geometry

21 pages, 7 figures

Scientific paper

We compute the open Gromov-Witten invariants for every compact semi-Fano toric surface, i.e. a toric surface X with nef anticanonical bundle. Unlike the Fano case, this involves non-trivial obstructions in the corresponding moduli problem. As an application, an explicit expression of the superpotential W for the mirror of X is obtained, which in turn gives an explicit ring presentation of the small quantum cohomology of X. We also give a computational verification of the natural ring isomorphism between the small quantum cohomology of X and the Jacobian ring of W.

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