  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.
