2011/05/03 by Miguel Abreu, Abreu, Miguel, Leonardo Macarini +1
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.GT #math.SG
paper · pdf · doi:10.48550/arxiv.1105.0640
26 pages, 13 figures. Version 2 with updated references. Version 3 inludes brief description of reduction in stages, expanded comments, added and updated references - to appear in Transactions of the AMS
openalex publication_date 2011/05/03 · arxiv created 2012/01/17 · arxiv updated 2012/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider two natural Lagrangian intersection problems in the context of symplectic toric manifolds: displaceability of torus orbits and of a torus orbit with the real part of the toric manifold. Our remarks address the fact that one can use simple cartesian product and symplectic reduction considerations to go from basic examples to much more sophisticated ones. We show in particular how rigidity results for the above Lagrangian intersection problems in weighted projective spaces can be combined with these considerations to prove analogous results for all monotone toric symplectic manifolds. We also discuss non-monotone and/or non-Fano examples, including some with a continuum of non-displaceable torus orbits.