Disk counting and wall-crossing phenomenon via family Floer theory
Hang Yuan
TL;DR
This paper applies wall-crossing formulas within non-archimedean SYZ mirror symmetry to compute superpotentials and Gromov-Witten invariants for specific Lagrangian tori in toric Fano manifolds, confirming previous results.
Contribution
It introduces a novel application of wall-crossing formulas in non-archimedean SYZ mirror symmetry to explicitly compute invariants for Chekanov-type Lagrangians.
Findings
Computed Landau-Ginzburg superpotential for Chekanov-type Lagrangians.
Calculated one-pointed open Gromov-Witten invariants in toric Fano compactifications.
Results agree with prior works by Auroux, Chekanov-Schlenk, and Pascaleff-Tonkonog.
Abstract
We use the wall-crossing formula in the non-archimedean SYZ mirror construction (arXiv: 2003.06106) to compute the Landau-Ginzburg superpotential and the one-pointed open Gromov-Witten invariants for a Chekanov-type Lagrangian torus in any smooth toric Fano compactification of C^n. It agrees with the works of Auroux, Chekanov-Schlenk, and Pascaleff-Tonkonog.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Geometry and complex manifolds · Mathematical Dynamics and Fractals