Linear webs and algebraization theorems of inverse-Abel and inverse-Reiss type
A \(d\)-web \(W (d)\) of codimension one in \((\mathbb{C}^n, 0)\) is given by \(d\) complex analytic foliations of codimension one of \((\mathbb{C}^n, 0)\) which are in general position. A web \(W (d)\) is called linear if the leaves of all its foliations are hyperplanes (or pieces of hyperplanes) in \((\mathbb{C}^n, 0)\). A linear web \(W (d)\) is called algebraic is it is associated by duality to a nondegenerate algebraic curve \(\Gamma\) of degree \(d\) of a projective space \(P^n\). The author characterizes linear webs \(W (d) \subset (\mathbb{C}^n, 0)\) by giving two necessary and sufficient conditions for \(W (d)\) to be linear. He also gives three explicit equivalent conditions under which a linear web \(W (d) \subset (\mathbb{C}^n, 0)\) is algebraic and obtains equations for \(\Gamma \subset P^n\) in this case.
scientific article; zbMATH DE number 1003885