Here we show that a Kupka component of a codimension 1 singular foliation of with not a square is a complete intersection. The result implies the existence of a meromorphic first integral of .
On considĂšre ici les feuilletages holomorphes singuliers de codimension 1 dans , avec une composante de Kupka compacte . On dĂ©montre que est une intersection complĂšte si nâest pas un carrĂ©.
@article{AIF_1995__45_4_1119_0, author = {Ballico, Edoardo}, title = {A splitting theorem for the {Kupka} component of a foliation of ${\bf C} {\bf P}^n,\,n\ge 6$. {Addendum} to a paper by {O.} {Calvo-Andrade} and {N.} {Soares}}, journal = {Annales de l'Institut Fourier}, pages = {1119--1121}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {45}, number = {4}, year = {1995}, doi = {10.5802/aif.1487}, zbl = {0831.58046}, mrnumber = {97h:32050}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1487/} }
TY - JOUR AU - Ballico, Edoardo TI - A splitting theorem for the Kupka component of a foliation of ${\bf C} {\bf P}^n,\,n\ge 6$. Addendum to a paper by O. Calvo-Andrade and N. Soares JO - Annales de l'Institut Fourier PY - 1995 SP - 1119 EP - 1121 VL - 45 IS - 4 PB - Association des Annales de lâinstitut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1487/ DO - 10.5802/aif.1487 LA - en ID - AIF_1995__45_4_1119_0 ER -
%0 Journal Article %A Ballico, Edoardo %T A splitting theorem for the Kupka component of a foliation of ${\bf C} {\bf P}^n,\,n\ge 6$. Addendum to a paper by O. Calvo-Andrade and N. Soares %J Annales de l'Institut Fourier %D 1995 %P 1119-1121 %V 45 %N 4 %I Association des Annales de lâinstitut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1487/ %R 10.5802/aif.1487 %G en %F AIF_1995__45_4_1119_0
Ballico, Edoardo. A splitting theorem for the Kupka component of a foliation of ${\bf C} {\bf P}^n,\,n\ge 6$. Addendum to a paper by O. Calvo-Andrade and N. Soares. Annales de l'Institut Fourier, Volume 45 (1995) no. 4, pp. 1119-1121. doi : 10.5802/aif.1487. https://aif.centre-mersenne.org/articles/10.5802/aif.1487/
[CS]Chern numbers of a Kupka component, Ann. Inst. Fourier, 44-4 (1994), 1237-1242. | Numdam | MR | Zbl
, ,[CL]Codimension one foliations in CPn n ℠3, with Kupka components, in : Complex analytic methods in dinamical systems, Astérisque (1994), 93-133. | Zbl
, ,[F]Ein Kriterium fĂŒr vollstĂ€ndige Durchsnitte, Invent. Math., 62 (1981), 393-401. | MR | Zbl
,[FL]Connectivity in algebraic geometry, in : Algebraic Geometry, Proceedings Chicago 1980, Lect. Notes in Math. 862, Springer-Verlag (1981), 26-92. | Zbl
, ,[GML]A structural stability of foliations with a meromorphic first integral, Topology, 30 (1990), 315-334. | Zbl
, ,[OSS]Vector bundles on complex projective spaces, Progress in Math., 3, BirkhÀuser, Basel, 1978. | Zbl
, , ,Cited by Sources: