Mendes, Luis Gustavo; Sebastiani, Marcos A property of rational surfaces. (Une propriété des surfaces rationnelles.) (French) Zbl 0917.14021 Ann. Fac. Sci. Toulouse, VI. Sér., Math. 7, No. 3, 549-550 (1998). Dans cette note nous montrons comment les résultats de M. Carnier [“Cremona transformations and foliations on the complex projective plane” in: Singularity theory, Trieste 1991, 153-172 (1995)] sur les systèmes de Pfaff analytiques de dimensions 1 sur le plan projectif \(\mathbb{C}\mathbb{P}^2\) impliquent le théorème suivant. Théorème. – Soit \(M\) une surface rationnelle. Alors il existe un ensemble fini \(p_1,\dots,p_k\) de points de \(\mathbb{C}\mathbb{P}^2\) \((p_i\neq p_j\) si \(i\neq j)\) tel que \(M\) est dominée par la surface obtenue en éclatant une fois chaque point \(p_j\), \(j=1,\dots,k\). MSC: 14J26 Rational and ruled surfaces 14E15 Global theory and resolution of singularities (algebro-geometric aspects) Keywords:rational surface; resolution of singularities PDF BibTeX XML Cite \textit{L. G. Mendes} and \textit{M. Sebastiani}, Ann. Fac. Sci. Toulouse, Math. (6) 7, No. 3, 549--550 (1998; Zbl 0917.14021) Full Text: DOI Numdam EuDML OpenURL References: [1] Carnicer ( M. ) . - Cremona transformations and foliations on the complex projectives plane , Singularity theory, Trieste (1991) , pp. 153 - 172 ; World Sci. Plublishing , River Edge, New Jersey ( 1995 ). MR 1378398 | Zbl 0944.32037 · Zbl 0944.32037 [2] Beauville ( A. ) Lettre à l’un des auteurs . This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.