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Pré-Publication, Document De Travail Année : 2008

Ordinary holomorphic webs of codimension one

Résumé

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 $\pi'(n,d)$ strictly smaller than the bound $\pi(n,d)$ of castelnuovo. This bound $\pi'(n,d)$ 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
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Dates et versions

hal-00137470 , version 1 (20-03-2007)
hal-00137470 , version 2 (13-10-2008)

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Vincent Cavalier, Daniel Lehmann. Ordinary holomorphic webs of codimension one. 2008. ⟨hal-00137470v2⟩
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