Theorem on the density of separatrix connections for polynomial foliations in $\mathbb CP^2$

D. S. Volk

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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 point 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.

UDC: 517.927.7+517.927.71+517.938

 English version: Journal of Mathematical Sciences (New York), 2008, 150:5, 2326–2334

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