THEOREM ON THE DENSITY OF SEPARATRIX CONNECTIONS FOR POLYNOMIAL FOLIATIONS IN CP~2

摘要

In this paper, we prove that in the space of polynomial foliations of a fixed degree of the complex two-dimensional space, foliations with separatrix connection, i.e., foliations in which any two distinct points have a common separatrix, are dense. The main tool of the proof is the analysis of the monodromy group of the foliation in a neighborhood of the infinitely distant point of the ambient projective space.