|
|||||
|
|
|
|
|
|
|
|
|
A formula equating
open and closed Gromov–Witten invariants and its applications
to mirror symmetry
Kwokwai Chan |
|
Vol. 254 (2011), No. 2, 275–293
|
Abstract |
|
We prove that open Gromov–Witten invariants for semi-Fano toric manifolds of the form X = ℙ(KY ⊕𝒪Y ), where Y is a toric Fano manifold, are equal to certain 1-pointed closed Gromov–Witten invariants of X. As applications, we compute the mirror superpotentials for these manifolds. In particular, this gives a simple proof for the formula of the mirror superpotential for the Hirzebruch surface F2. |
Keywords
Open Gromov–Witten invariants, semi-Fano, toric manifolds,
mirror symmetry, Landau–Ginzburg model, superpotential
|
Mathematical Subject Classification 2010
Primary: 53D45, 53D37
Secondary: 53D12, 14M25, 14N35
|
Milestones
Received: 21 October 2010
Revised: 3 March 2011
Accepted: 27 April 2011
Published: 27 February 2012
|
Authors |
| Kwokwai Chan | |
| Department of Mathematics The Chinese University of Hong Kong Shatin Hong Kong |
|
|
