  Superstrings and topological strings with supermanifolds as target space play
a central role in the recent developments in string theory. Nevertheless the
rules for higher-genus computations are still unclear or guessed in analogy
with bosonic and fermionic strings. Here we present a common geometrical
setting to develop systematically the prescription for amplitude computations.
The geometrical origin of these difficulties is the theory of integration of
superforms. We provide a translation between the theory of supermanifolds and
topological strings with supertarget space. We show how in this formulation one
can naturally construct picture changing operators to be inserted in the
correlation functions to soak up the zero modes of commuting ghost and we
derive the amplitude prescriptions from the coupling with an extended
topological gravity on the worldsheet. As an application we consider a simple
model on R^(3|2) leading to super-Chern-Simons theory.
