an:00566972
Zbl 0792.58001
Mendes, L. G.; Sebastiani, M.
On the density of the Pfaffian systems without algebraic solution
FR
Ann. Inst. Fourier 44, No. 1, 271-276 (1994).
00019547
1994
j
58A17 57R30 32S65 32S05 37C85
holomorphic foliations; projective rational surface
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 alg??briques' (1979; Zbl 0477.58002)].
L.G.Mendes and M.Sebastiani (Porto Alegre)
Zbl 0625.57012; Zbl 0477.58002