The Euler-Betti Algorithm to identify foliations in Hilbert Scheme

Abstract

Foliations in the complex projective plane are uniquely determined by their singular locus, which is in correspondence with a zero-dimensional ideal. However, this correspondence is not surjective. We give conditions to determine whether an ideal arises as the singular locus of a foliation or not. Furthermore, we give an effective method to construct the foliation in the positive case.