Luengo Velasco, Ignacio and Olivares , J.
(2000)
*Germs of holomorphic vector fields in C-m without a separatrix.*
Transactions of the American Mathematical Society, 352
(12).
pp. 5511-5524.
ISSN 0002-9947

PDF
Restricted to Repository staff only 1MB |

Official URL: http://www.jstor.org/stable/221900

## Abstract

We prove the existence of families of germs of holomorphic vector fields in Cm without a separatrix, in every complex dimension m bigger than or equal to 4.

Item Type: | Article |
---|---|

Additional Information: | Supported by DGICYT (Spain) PB97-0284-C02-01.Partially supported by CONACYT (Mexico) Projects 3398-E9307, 0324P-E9506 and Postdoctoral Grant 963052, at Dto. Algebra, Geometria y Topologia, U. Valladolid. |

Uncontrolled Keywords: | Holomorphic vector fields; Separatrix |

Subjects: | Sciences > Mathematics > Algebra |

ID Code: | 16775 |

References: | C. Camacho, P. Sad, Invariant varieties through singularities of holomorphic vector fields. Ann. of Math. 115 (1982), 579-595. MR 83m:58062 S.S. Chern, Meromorphic vector fields and characteristic numbers. Scripta Math. 29 (1973), 243-251. MR 54:609 Ph. Griffiths, J. Harris, Principles of Algebraic Geometry, Wiley-Interscience, 1978. MR 80b:14001; Reprint MR 95d:14001 X. Gomez-Mont, G. Kempf, Stability of meromorphic vector fields in projective spaces. Comment. Math. Helv. 64 (1989), 462-473. MR 90d:14012 X. Gomez-Mont, I. Luengo, Germs of holomorphic vector fields in C3 without a separatrix. Invent. Math. 109 (1992), 211-219. MR 93m:32049 R. Hartshorne, Algebraic Geometry, Graduate Texts in Math., 52 Springer-Verlag, New York, Heidelberg, 1977. MR 57:3116 J. Olivares, On vector fields in C3 without a separatrix. Rev. Mat. Univ. Complut. Madrid. 5 (1992), 13-34. MR 94a:32057 J. Olivares, On the problem of existence of germs of holomorphic vector fields in C'm, without a separatrix, (m > 3). Ecuaciones Diferenciales, Singularidades (J. Mozo Fernandez ed.), Secretariado de publicaciones e intercambio cientffico, Universidad de Valladolid, Serie Ciencias 15, 1997, pp. 317-351. I.R. Shafarevich, Basic Algebraic Geometry Varieties in projective space, 2nd edition, Springer-Verlag, 1994. MR 95m:14001 |

Deposited On: | 19 Oct 2012 08:14 |

Last Modified: | 27 Nov 2012 16:18 |

Repository Staff Only: item control page