In many physical and geometric applications, a supermanifold comes equipped with an Grassmann-odd symplectic structure. All natural geometric objects on a supermanifold are graded. In particular, the bundle of two-forms is equipped with a grading. An odd symplectic form ω on a supermanifold is a closed, odd form, inducing a non-degenerate pairing on "TM". Such a supermanifold is called a P-manifold. Its graded dimension is necessarily "(n,n)", because the odd symplectic form induces a pairing of odd and even variables. There is a version of the Darboux theorem for P-manifolds, which allows one