Tissus linéaires et théorèmes d'algébrisation de type Abdel-inverse et Reiss-inverse

Abstract

A d-web in (\(\mathbb{C}^n \),0) is given by d complex analytic foliations of codimension one in (\(\mathbb{C}^n \),0) which are in general position. A d-web \(\mathcal{L}(d)\) in (\(\mathbb{C}^n \),0) is linear if all the leaves are (pieces of) hyperplanes in \(\mathbb{C}^n \) and \(\mathcal{L}(d)\) is algebraic if it is associated, by duality, to a nondegenerate algebraic curve Г in \(\mathbb{P}^n \) of degree d. We characterize linear webs in (\(\mathbb{C}^n \),0). We give explicit conditions under which a linear d-web in (\(\mathbb{C}^n \),0) is algebraic and we obtain equations for \(\Gamma \subset \mathbb{P}^n \) in this case. Some related problems are discussed and some questions are posed.