On Complex Supermanifolds with Trivial Canonical Bundle
  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. 
Josua Groeger
math-ph hep-th math.AG math.DG math.MP