English

Non-displaceable toric fibers on compact toric manifolds via tropicalizations

Symplectic Geometry 2015-07-23 v1 Algebraic Geometry

Abstract

We give a combinatorial way to locate non-displaceable Lagrangian toric fibers on compact toric manifolds. By taking the intersection of certain tropicalizations coming from combinatorial data of a moment polytope, we locate all strongly bulk-balanced fibers introduced in [FOOOSurv]. As an application, we show that every bulk-balanced fiber defined in [FOOOToric2] is strongly bulk-balanced. Thus, the method indeed detects the positions of all non-displaceable fibers that can be detected by Lagrangian Floer theory developed in [FOOOToric1] and [FOOOToric2].

Keywords

Cite

@article{arxiv.1507.06132,
  title  = {Non-displaceable toric fibers on compact toric manifolds via tropicalizations},
  author = {Yoosik Kim and Jaeho Lee},
  journal= {arXiv preprint arXiv:1507.06132},
  year   = {2015}
}

Comments

28 pages, 7 figures