Hypersurfaces symplectiques réelles et pinceaux de Lefschetz réels

Damien Gayet (1)

1 ICJ - Institut Camille Jordan

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 Poincaré 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.

Domaines: Géométrie symplectique [math.SG]

Damien Gayet. Hypersurfaces symplectiques réelles et pinceaux de Lefschetz réels. 2006. ⟨hal-00115876v1⟩