Weakly Lefschetz symplectic manifolds.

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Fernández, M. and Muñoz, Vicente and Ugarte, L. (2007) Weakly Lefschetz symplectic manifolds. Transactions of the American Mathematical Society, 359 (4). pp. 1851-1873. ISSN 0002-9947

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Official URL: http://www.ams.org/journals/tran/2007-359-04/S0002-9947-06-04114-6/S0002-9947-06-04114-6.pdf




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 CPm of the complex projective space CPm along weakly Lefschetz symplectic submanifolds M ⊂ CPm. As an application we
construct, for each even integer s ≥ 2, compact symplectic manifolds which are s–Lefschetz but not (s + 1)–Lefschetz.


Item Type:Article
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:21090
Deposited On:29 Apr 2013 15:33
Last Modified:12 Dec 2018 15:13

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