On the density of the Pfaffian systems without algebraic solution
Let \(M\) be an analytic surface. \textit{A. Lins Neto} [J. Differ. Geom. 26, 1-31 (1987; Zbl 0625.57012)] introduced a topology in the set \(\Pi(M)\) of holomorphic foliations with isolated singularities on \(M\). \(\Omega \in \Pi(M)\) is ``rigid'' if it is an isolated point of \(\Pi(M)\). In our paper it is proved that if \(M\) is a projective rational surface non-isomorphic to \(\mathbb{P}_ 2(\mathbb{C})\) then there exists \(\Omega \in \Pi(M)\) rigid and having algebraic leaves. The case of \(\mathbb{P}_ 2(\mathbb{C})\) has been considered by \textit{J. P. Jouanolou} [`Equations de Pfaff algébriques' (1979; Zbl 0477.58002)].
scientific article; zbMATH DE number 566972