Hypersurfaces symplectiques réelles et pinceaux de Lefschetz réels

Details Hypersurfaces symplectiques réelles et pinceaux de Lefschetz réels Hypersurfaces symplectiques réelles et pinceaux de Lefschetz réels

2006-11-24

arxiv.org/abs/math/0611746v2

Mathematics

Symplectic Geometry

A new version wich includes the higher rank bundles, and a kind of uniqueness. To appear in the Journal of Symplectic Geometry

Scientific paper

In a compact, symplectic real manifold, i.e supporting an antisymplectic involution, we use Donaldson's construction to build a codimension 2 symplectic submanifold invariant under the action of the involution. If the real part of the manifold is not empty, and if the symplectic form $\om$ is entire, then for all $k$ big enough, we can find a hypersurface Poincar\'e dual of $k[\omega]$ such that its real part has at least $k^{\dim X/4}$ connected components, up to a constant independant of $k$. Finally we extend to our real case Donaldson's construction of Lefschetz pencils.

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