ABSTRACT
By a complex space we mean a reduced, not necessarily irreducible, complex analytic space.
Let X be a complex space. We denote by CX the constant sheaf on X . When X is smooth we denote by E·X the De Rham complex of differential forms on X . Our goal is to define a complex Λ·X on X (in fact, as we shall see, a family of complexes) which replaces, in the singular case, the De Rham complex. Let us consider a resolution of singularities of X , i.e. a commutative diagram:
E˜ i
X˜
E j
X
(2.1)
where E ⊂ X is a nowhere dense closed subspace, containing the singularities of X , j : E → X is the natural inclusion, X˜ is a smooth manifold and π is a proper modification inducing an isomorphism X˜ \ E˜ X \ E.
