Hypersurfaces symplectiques réelles et pinceaux de Lefschetz réels

2006/11/24 by Damien Gayet, Gayet, Damien
Mathematics · #14D06 #14P25 #32Q15. #53D05 #FOS: Mathematics #Symplectic Geometry (math.SG) #math.SG #msc:14D06 #msc:14P25 #msc:32Q15. #msc:53D05

paper · pdf · doi:10.48550/arxiv.math/0611746

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

arxiv created 2007/12/06 · arxiv updated 2009/12/01

Abstract

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[ω] 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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