  We give an algebraic characterisation for the triviality of the canonical
bundle of a complex supermanifold in terms of a certain Batalin-Vilkovisky
superalgebra structure. As an application, we study the Calabi-Yau case, in
which an explicit formula in terms of the Levi-Civita connection is achieved.
Our methods include the use of complex integral forms and the recently
developed theory of superholonomy.
