Covariant symplectic structure of the complex Monge-Ampere equation

The complex Monge-Ampere equation is invariant under arbitrary holomorphic changes of the independent variables with unit Jacobian. We present its variational formulation where the action remains invariant under this infinite group. The new Lagrangian enables us to obtain the first symplectic 2-form for the complex Monge-Ampere equation in the framework of the covariant Witten-Zuckerman approach to symplectic structure. We base our considerations on a reformulation of the Witten-Zuckerman theory in terms of holomorphic differential forms. The first closed and conserved Witten-Zuckerman symplectic 2-form for the complex Monge-Ampere equation is obtained in arbitrary dimension and for all cases elliptic, hyperbolic and homogeneous.