ABSTRACT
In this chapter we define and study differential forms on a complex manifold which have logarithmic poles along a divisor with normal crossing.
Let X be a compact complex manifold of complex dimension n = dimCX and D = D1∪· · ·∪DN is a divisor with normal crossing ; that means that each Di is a smooth hypersurface of X , and at each point x ∈ X , there are at most n divisors Dj passing through x and which are transversal. In particular, given x, one can find complex analytic coordinates (z1, . . . , zn) in a neighborhood U of x, such that the local equation of D∩U in U is z1 · · · zs = 0, s depending on x.
