A symplectic form on the space of embedded symplectic surfaces and its reduction by reparametrizations

Let (M, ω) be a symplectic manifold, and (Σ, σ) a closed connected symp-lectic 2-manifold. We construct a weakly symplectic form ω^D on C∞(Σ, M) which is a special case of Donaldson's form. We show that the restriction of ω^D to any orbit of the group of Hamiltonian symplectomorphisms through a symplectic embedding (Σ, σ) (M, ω) descends to a weakly symplectic form on the quotient by Sympl(Σ, σ), and that the symplectic space obtained is a symplectic quotient of the subspace of symplectic embeddings with respect to the Sympl(Σ, σ)-action. We also compare ω^D to another 2-form. We conclude with a result on the restriction of ω^D to moduli spaces of holomorphic curves.