English

Seidel elements and potential functions of holomorphic disc counting

Symplectic Geometry 2018-08-02 v2 Algebraic Geometry

Abstract

Let M be a symplectic manifold equipped with a Hamiltonian circle action and let L be an invariant Lagrangian submanifold of M. We study the problem of counting holomorphic disc sections of the trivial M-bundle over a disc with boundary in L through degeneration. We obtain a conjectural relationship between the potential function of L and the Seidel element associated to the circle action. When applied to a Lagrangian torus fibre of a semi-positive toric manifold, this degeneration argument reproduces a conjecture (now a theorem) of Chan-Lau-Leung-Tseng relating certain correction terms appearing in the Seidel elements with the potential function.

Keywords

Cite

@article{arxiv.1301.5454,
  title  = {Seidel elements and potential functions of holomorphic disc counting},
  author = {Eduardo Gonzalez and Hiroshi Iritani},
  journal= {arXiv preprint arXiv:1301.5454},
  year   = {2018}
}

Comments

38 pages, v2: more details added in the proof of Lemma 3.15

R2 v1 2026-06-21T23:14:03.336Z