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

 

Weakly Lefschetz symplectic manifolds


Authors: M. Fernández, V. Muñoz and L. Ugarte
Journal: Trans. Amer. Math. Soc. 359 (2007), 1851-1873
MSC (2000): Primary 53D05, 57R17, 53D35, 53C15
Published electronically: October 17, 2006
MathSciNet review: 2272152
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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.


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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
Email: ugarte@unizar.es

DOI: http://dx.doi.org/10.1090/S0002-9947-06-04114-6
PII: S 0002-9947(06)04114-6
Received by editor(s): February 9, 2005
Published electronically: October 17, 2006
Article copyright: © Copyright 2006 American Mathematical Society