2017/03/10 by Dufour, Jean Paul, Lehmann, Daniel
#53A60 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1703.03725
We are interested by holomorphic d-webs W of codimension one in a complex n-dimensional manifold M. If they are ordinary, i.e. if they satisfy to some condition of genericity (whose precise definition is recalled), we proved in [CL] that their rank ρ(W) is upper-bounded by a certain number π'(n,d) (which, for n≥ 3, is stictly smaller than the Castelnuovo-Chern's bound π(n,d)). In fact, denoting by c(n,h) the dimension of the space of homogeneous polynomials of degree h with n unknowns, and by h0 the integer such that c(n,h0-1)