Remarks on Lagrangian intersections in toric manifolds
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- by Miguel Abreu and Leonardo Macarini PDF
- Trans. Amer. Math. Soc. 365 (2013), 3851-3875 Request permission
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.References
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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
- 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).
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 3851-3875
- MSC (2010): Primary 53D12; Secondary 53D20
- DOI: https://doi.org/10.1090/S0002-9947-2012-05791-6
- MathSciNet review: 3042606