Smooth points of the space of plane foliations with a center

Abstract

We prove that a logarithmic foliation corresponding to a generic line arrangement of $d+1\ge 3$ lines in the complex plane, with pairwise natural and co-prime residues, is a smooth point of the center set of plane foliations (vector fields) of degree $d$.

arXiv commentThe introduction and the last section has been changed. Many typos are corrected