2007/03/20 by Vincent Cavalier, Daniel Lehmann, Cavalier, Vincent +1
Mathematics · #57R25 #58A20 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematics and Applications #math.DS #msc:57R25 #msc:58A20
paper · pdf · doi:10.48550/arxiv.math/0703596
13 pages
openalex publication_date 2007/03/20 · arxiv created 2008/10/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main change with respect to the previous version is a change of terminology : we call "ordinary" the webs previously called "regular". A holomorphic d-web of codimension one in dimension n is "ordinary", if it satisfies to some condition of genericity. In dimension at least 3, any such web has a rank bounded from above by a number π'(n,d) strictly smaller than the bound π(n,d) of castelnuovo. This bound π'(n,d) is optimal. Moreover, for some d's, the abelian relations are sections with vanishing covariant derivative of some bundle with a connection, the curvature of which generalizes the Blaschke curvature. In dimension 2, we recover results of Hénaut and Pantazi