Combinatorics of line arrangements and dynamics of polynomial vector fields

Original · EN

Let A be a real line arrangement and D(A) the module of A--derivations. First, we give a dynamical interpretation of D(A) as the set of polynomial vector fields which posses A as invariant set. We characterize polynomial vector fields having an infinite number of invariant lines. Then we prove that the minimal degree of polynomial vector fields fixing only a finite set of lines in D(A) is not determined by the combinatorics of A.