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REMARKS ON LAGRANGIAN INTERSECTIONS IN TORIC MIGUEL ABREU AND LEONARDO MACARINI
 

Summary: REMARKS ON LAGRANGIAN INTERSECTIONS IN TORIC
MANIFOLDS
MIGUEL ABREU AND LEONARDO MACARINI
Abstract. 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.
1. Introduction
Let (M2n
, ) be a toric symplectic manifold, i.e. a symplectic manifold equipped with
an effective Hamiltonian Tn
-action generated by a moment map
µ : M P := µ(M) (Rn
)
,

  

Source: Abreu, Miguel - Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa

 

Collections: Mathematics