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Let (M,\omega) be a symplectic manifold, and (\Sigma,\sigma) a closedconnected symplectic 2-manifold. We construct a weakly symplectic form{\omega^{D}}_{(\Sigma, \sigma)} on the space of immersions \Sigma \to M that isa special case of Donaldson's form. We show that the restriction of{\omega^{D}}_{(\Sigma,\sigma)} to any orbit of the group of Hamiltoniansymplectomorphisms through a symplectic embedding (\Sigma,\sigma) \to(M,\omega) descends to a weakly symplectic form \omega^D_{\red} on the quotientby Sympl(\Sigma,\sigma), and that the obtained symplectic space is a symplecticquotient of the subspace of symplectic embeddings S_{e}(\Sigma,\sigma) withrespect to the Sympl(\Sigma,\sigma)-action. We also compare{\omega^{D}}_{(\Sigma,\sigma)} and its reduction \omega^D_{\red} to another2-form on the space of immersed symplectic \Sigma-surfaces in M. We conclude bya result on the restriction of {\omega^{D}}_{(\Sigma,\sigma)} to moduli spacesof J-holomorphic curves.

Symplectic forms on the space of embedded symplectic surfaces and their reductions