Biblioteca de la Universidad Complutense de Madrid

Completeness is determined by any non-algebraic trajectory

Impacto

Bustinduy Candelas, Álvaro y Giraldo Suárez, Luis (2012) Completeness is determined by any non-algebraic trajectory. Advances in Mathematics, 231 (2). pp. 664-679. ISSN 0001-8708

[img] PDF
Restringido a Sólo personal autorizado del repositorio hasta 31 Diciembre 2020.

263kB

URL Oficial: http://www.sciencedirect.com/science/article/pii/S0001870812001910




Resumen

It is proved that any polynomial vector field in two complex variables which is complete on a non-algebraic trajectory is complete.


Tipo de documento:Artículo
Palabras clave:Complete vector field; Complex orbit; Holomorphic foliation
Materias:Ciencias > Matemáticas > Geometría
Ciencias > Matemáticas > Topología
Código ID:16463
Referencias:

M. Brunella, Sur les courbes int´egrales propres des champs de vecteurs polynomiaux, Topology 37 (6) (1998) 1229–1246.

M. Brunella, Birational geometry of foliations, in: First Latin American Congress of Mathematicians, IMPA, 2000.

M. Brunella, Foliations on complex projective surfaces, in: Pubblicazioni del Centro di Ricerca Matematica Ennio de Giorgi. Proceedings, 2003, pp. 49–77.

M. Brunella, Complete vector fields on the complex plane, Topology 43 (2) (2004) 433–445.

M. Brunella, Uniformisation of foliations by curves, in: Lecture Notes in Math., 1998, 2010, pp. 105–163.

A. Bustinduy, On the entire solutions of a polynomial vector field on C2, Indiana Univ. Math. J. 53 (2004) 647–666.

A. Bustinduy, The completeness of a polynomial vector field is determined by a transcendental trajectory, J. Differential Equations 227 (2006) 282–300.

A. Bustinduy, Complete holomorphic vector fields on C2 whose underlying foliation is polynomial, Int. J. Math. 21 (3) (2010) 333–347.

E. Ghys, Feuilletages holomorphes de codimension un sur les espaces homog´enes complexes, Ann. Fac. Sci. Toulouse, VI. S´er., Math 5 (3) (1996) 493–519.

P. Griffiths, Variations on a theorem of Abel, Invent. Math 35 (1976) 321–390.

S. Lang, Introduction to Complex Hyperbolic Spaces, Springer-Verlag, 1987.

J. Martinet, J.-P. Ramis, Problemes de modules pour des ´equations diffe´erentielles non lin´eaires du premier ordre, Publications IHES 55 (1982) 63–164.

M. McQuillan, Non-commutative Mori Theory, 2001. Preprint IHES, M/01/42.

J. Milnor, Dynamics in One Complex Variable, third ed., in: Annals of Mathematics Studies, vol. 160, Princeton University Press, Princeton and Oxford, 2006.

I. Pan, M. Sebastiani, Les ´equations diff´erentielles alg´ebriques et les singularit´es mobiles, in: Ensaios Matem´aticos, vol. 8, Sociedade Brasileira de Matem´atica, 2004.

P. Petersen, Riemannian geometry, in: Graduate Texts in Mathematics, vol. 171, Springer, New York, 2006.

M. Suzuki, Propri´et´es topologiques des polynˆomes de deux variables complexes, et automorphismes alg´ebriques de l’espace C2, J. Math. Soc. Japan 26 (1974) 241–257.

M. Suzuki, Sur les op´erations holomorphes du groupe additif complexe sur l’espace de deux variables complexes, Ann. Sci. ´ Ecole Norm. Sup. 10 (4) (1977) 517–546.

Depositado:20 Sep 2012 07:47
Última Modificación:20 Sep 2012 07:47

Sólo personal del repositorio: página de control del artículo