Lagrangian Floer potential of orbifold spheres

Abstract

For each sphere with three orbifold points, we construct an algorithm to compute the open Gromov-Witten potential, which serves as the quantum-corrected Landau-Ginzburg mirror and is an infinite series in general. This gives the first class of general-type geometries whose full potentials can be computed. As a consequence we obtain an enumerative meaning of mirror maps for elliptic curve quotients. Furthermore, we prove that the open Gromov-Witten potential is convergent, even in the general-type cases, and has an isolated singularity at the origin, which is an important ingredient of proving homological mirror symmetry.

65 pages, 43 figures

References in corpus (1)

• Localized mirror functor for Lagrangian immersions, and homological mirror symmetry for P^1_{a,b,c}

Cited by in corpus (6)

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• Localized mirror functor for Lagrangian immersions, and homological mirror symmetry for P^1_{a,b,c}
• Localized mirror functor constructed from a Lagrangian torus
• On quantum cohomology ring of elliptic ${\mathbb{P}}^1$ orbifolds
• On the modularity of certain functions from the Gromov-Witten theory of elliptic orbifolds