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World Scientific Publishing, International Journal of Mathematics, 01(30), p. 1950003, 2019

DOI: 10.1142/s0129167x19500034

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Detecting non-displaceable toric fibers on compact toric manifolds via tropicalizations

Journal article published in 2019 by Yoosik Kim ORCID, Jaeho Lee, Fumihiko Sanda
This paper was not found in any repository, but could be made available legally by the author.
This paper was not found in any repository, but could be made available legally by the author.

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Abstract

We provide a combinatorial way to locate non-displaceable Lagrangian toric fibers on any compact toric manifold. By taking the intersection of certain tropicalizations coming from its moment polytope, one can detect all Lagrangian toric fibers having non-vanishing Floer cohomology ([K. Fukaya, Y.-G. Oh, H. Ohta and K. Ono, Lagrangian Floer theory on compact toric manifolds, I, Duke Math. J. 151(1) (2010) 23–174; K. Fukaya, Y.-G. Oh, H. Ohta and K. Ono, Lagrangian Floer theory on compact toric manifolds II: bulk deformations, Selecta Math. (N.S.) 17(3) (2011) 609–711.]). The intersection completely characterizes all non-displaceable toric fibers, in some cases including pseudo symmetric smooth Fano varieties ([G. Ewald, On the classification of toric Fano varieties, Discrete Comput. Geom. 3(1) (1988) 49–54.]).