Weakly Lefschetz symplectic manifolds

Fernandez, Marisa; Munoz, Vicente; Ugarte, Luis

Weakly Lefschetz symplectic manifolds

Authors

Fernandez, Marisa

Munoz, Vicente

Ugarte, Luis

Description

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.
22 pages; many improvements from previous version