Weakly Lefschetz symplectic manifolds
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- by M. Fernández, V. Muñoz and L. Ugarte PDF
- Trans. Amer. Math. Soc. 359 (2007), 1851-1873 Request permission
Abstract:
For a symplectic manifold, the harmonic cohomology of symplectic divisors (introduced by Donaldson, 1996) and of the more general symplectic zero loci (introduced by Auroux, 1997) are compared with that of its ambient space. We also study symplectic manifolds satisfying a weakly Lefschetz property, that is, the $s$–Lefschetz property. In particular, we consider the symplectic blow-ups $\widetilde {CP}{}^m$ of the complex projective space ${CP}^m$ along weakly Lefschetz symplectic submanifolds $M\subset {CP}^m$. As an application we construct, for each even integer $s\geq 2$, compact symplectic manifolds which are $s$–Lefschetz but not $(s+1)$–Lefschetz.References
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Additional Information
- M. Fernández
- Affiliation: Departamento de Matemáticas, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain
- Email: marisa.fernandez@ehu.es
- V. Muñoz
- Affiliation: Departamento de Matemáticas, Consejo Superior de Investigaciones Científicas, C/ Serrano 113bis, 28006 Madrid, Spain
- Email: vicente.munoz@imaff.cfmac.csic.es
- L. Ugarte
- Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Zaragoza, Campus Plaza San Francisco, 50009 Zaragoza, Spain
- MR Author ID: 614982
- Email: ugarte@unizar.es
- Received by editor(s): February 9, 2005
- Published electronically: October 17, 2006
- © Copyright 2006 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 359 (2007), 1851-1873
- MSC (2000): Primary 53D05, 57R17, 53D35, 53C15
- DOI: https://doi.org/10.1090/S0002-9947-06-04114-6
- MathSciNet review: 2272152