Weakly Lefschetz symplectic manifolds

Details Weakly Lefschetz symplectic manifolds Weakly Lefschetz symplectic manifolds

2004-04-27

arxiv.org/abs/math/0404479v2

Mathematics

Symplectic Geometry

22 pages; many improvements from previous version

Scientific paper

The harmonic cohomology of a Donaldson symplectic submanifold and of an Auroux symplectic submanifold are compared with that of its ambient space. We also study symplectic manifolds satisfying a weakly Lefschetz property, that is, the $s$-Lefschetz propery. In particular, we consider the symplectic blow-ups of the complex projective space along weakly Lefschetz symplectic submanifolds. 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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