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arXiv · 1507.06132

Non-displaceable toric fibers on compact toric manifolds via tropicalizations

Yoosik Kim·Jaeho Lee
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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].

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Yoosik Kim, Jaeho Lee. 2015-07-22. Non-displaceable toric fibers on compact toric manifolds via tropicalizations. https://arxiv.org/abs/1507.06132

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