Nonorientable polynomial foliations on the plane (Q756206)

Let \({\mathcal F}_ n\) be the space of 2-forms \(w=a dy^ 2+b dx dy+c dx^ 2\) on \({\mathbb{R}}^ 2\), where a, b, c are polynomials of degree less than or equal to n and such that \(b^ 2-4ac\geq 0\) and \((b^ 2-4ac)^{- 1}(0)=a^{-1}(0)\cap b^{-1}(0)\cap c^{-1}(0);\) \({\mathcal F}_ n\) is endowed with the \(C^ 1\)-Whitney topology. The author shows that there exists an open subset \({\mathcal S}_ n\) of \({\mathcal F}_ n\) consisting of structurally stable forms. In addition, if \(n=1\) or \(n=2\), he proves that \({\mathcal S}_ n\) is dense in \({\mathcal F}_ n\).