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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Remarks on Lagrangian intersections in toric manifolds


Authors: Miguel Abreu and Leonardo Macarini
Journal: Trans. Amer. Math. Soc. 365 (2013), 3851-3875
MSC (2010): Primary 53D12; Secondary 53D20
Published electronically: December 17, 2012
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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.


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Additional Information

Miguel Abreu
Affiliation: Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
Email: mabreu@math.ist.utl.pt

Leonardo Macarini
Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, Cidade Universitária, CEP 21941-909, Rio de Janeiro, Brazil
Email: leonardo@impa.br

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05791-6
PII: S 0002-9947(2012)05791-6
Received by editor(s): May 11, 2011
Received by editor(s) in revised form: December 5, 2011
Published electronically: December 17, 2012
Additional Notes: The authors were partially supported by Fundação para a Ciência e a Tecnologia (FCT/Portugal), Fundação Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES/Brazil) and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq/Brazil).
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.