Regular holomorphic webs of codimension one

Given a d-web of codimension one on a holomorphic n-dimensional manifold M0 (d > n), we assume that, at any point of M0, the d hyperplanes tangent to the local foliations at a point of M0 are distinct, and that there exists n of them in general position (but we do not require any n of them to be in general position). For such a web, we shall define some specific analytical subset S of M0 which -genericallyhas dimension ≤ n− 1 or is empty : in this case the web will be said “regular”; when -exceptionallythe set S is n-dimensional, the web will be said “special”. We prove that the rank of regular d-webs has an upper-bound π(n, d) which, for n ≥ 3, is strictly smaller than the bound π(n, d) of Castelnuovo (the maximal arithmetical genus of an algebraic curve of degree d in the complex n-dimensional projective space Pn). Let c(n, h) denote the dimension of the vector space of homogeneous polynomials of degree h in n variables. The number π(n, d) is then equal to 0 for d < c(n, 2), and to P