Singular 2 webs and Polar Curves

Abstract

A 2-web in the plane is given by two everywhere transverse 1-foliations. In this paper we introduce the study of singular 2-webs, given by any two foliations, which may be tangent in some points. We show that such two foliations are tangent along a curve, which will be called the polar curve of the 2-web, and we study the relationship between the contact order of leaves of both foliations and the singularities of the polar curve.