Global stucture of webs in codimension one.

Vincent Cavalier (1) , Daniel Lehmann (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We describe the global structure of holomorphic webs in codimension one, and in particular their singularity (caustic). Various concepts are introduced, which have no interest locally near a regular point, such as the type, the reducibility, the quasi-smoothness, the CI property (complete intersection), the dicriticity... We prove for instance that the algebraicity of a web globally defined on a complex projective space may be readen on its caustic (dicriticity), at least if each irreducible component is CI, and the web quasi-smooth. .

Mots clés: web; quasi-smoothness; dicriticity; algebraicity

Domaines: Systèmes dynamiques [math.DS]; Géométrie différentielle [math.DG]; Géométrie algébrique [math.AG]

Vincent Cavalier, Daniel Lehmann. Global stucture of webs in codimension one.. 2008. ⟨hal-00264473⟩