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Hypersurfaces symplectiques réelles et pinceaux de Lefschetz réels

Damien Gayet
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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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Damien Gayet. 2007-12-06. Hypersurfaces symplectiques réelles et pinceaux de Lefschetz réels. https://arxiv.org/abs/math/0611746

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