Smooth Points of the Space of Plane Foliations with a Center.

We prove that a logarithmic foliation corresponding to a generic line arrangement of |$d+1 \geq 3$| 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 |$d$|⁠. [ABSTRACT FROM AUTHOR]