Let
be a symplectic manifold, and
a closed connected symplectic
-manifold. We construct
a weakly symplectic form
on
which is a special case of Donaldson’s form. We show that the restriction
of
to any orbit of the group of Hamiltonian symplectomorphisms through a symplectic
embedding
descends to a weakly symplectic form on the quotient by
, and that the symplectic
space obtained is a symplectic quotient of the subspace of symplectic embeddings with respect to
the
-action. We also
compare
to another
-form. We conclude with a
result on the restriction of
to moduli spaces of holomorphic curves.
Keywords
symplectic manifold, Donaldson's form, symplectic quotient,
moduli space of J-holomorphic curves