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This paper follows a previous one in which were introduced deformationinvariants $\chi^d_r$, $d \in H_2 (X ; \Z)$, $r \in \N$, of closed realsymplectic four-manifolds $(X, \omega, c_X)$, invariants which produced lowerbounds in real enumerative geometry. We prove here using methods of symplecticfield theory that the lower bounds are sharp when $r \leq 1$ and the real locusof the manifold contains a sphere, torus or real projective plane (understronger assumptions in this last case). We also prove that a big power of twodivides $\chi^d_r$ as soon as r is not too big and when the real locus containsa sphere or real projective plane (under the same stronger assumptions in thislast case). We finally present some explicit computations in the case of theprojective plane or quadric ellipsoid surface as well as the general formulasused to get them, formulas which involve some relative invariants that we firstdefine.

Optimalit\'e, congruences et calculs d'invariants des vari\'et\'es symplectiques r\'eelles de dimension quatre