 However, graded manifolds are characterized by sheaves on smooth manifolds, while supermanifolds are constructed by gluing of sheaves of supervector spaces.A graded manifold of dimension formula_1 is defined as a locally ringed space formula_2 where formula_3 is an formula_4-dimensional smooth manifold and formula_5 is a formula_6-sheaf of Grassmann algebras of rank formula_7 where formula_6 is the sheaf of smooth real functions on formula_3.The sheaf formula_5 is called the structure sheaf of the graded manifold formula_2, and the manifold formula_3 is said to be the body of formula_2.