2015/07/22 by Yoosik Kim, Jaeho Lee, Kim, Yoosik +1
Mathematics · #14T05 #53D40 #Algebraic Geometry (math.AG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.AG #math.SG #msc:14T05 #msc:53D40
paper · pdf · doi:10.48550/arxiv.1507.06132
28 pages, 7 figures
arxiv created 2015/07/22 · arxiv updated 2015/07/23
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].