Feuilletages holomorphes sur les surfaces complexes compactes

Brunella, Marco

doi:10.1016/s0012-9593(97)89932-6

Cited by 72 publications

(101 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The map a is a germ of an isomorphism with cr(0) = On-iWe associate to the germ -F a compact complex surface in the following way. We have a sequence of blowing-ups over the ball B One can suppose that a is denned in a neighbourhood of the closed unit ball B C C 2 and that a(B) is relatively compact in B^-\. Let B 1 CC B be a slightely smaller ball.…”

Section: Surfaces With Global Spherical Shellsmentioning

confidence: 99%

See 1 more Smart Citation

Vector fields and foliations on compact surfaces of class ${\rm VII}_0$

Dloussky¹,

Oeljeklaus²

1999

Annales De L’institut Fourier

View full text Add to dashboard Cite

Section: Surfaces With Global Spherical Shellsmentioning

confidence: 99%

“…We recall that in a(S) two successive singular sequences 5p=(p+2,2,..., 2) are separated by at most one regular sequence r^=(2,...,2).…”

mentioning

confidence: 99%

Vector fields and foliations on compact surfaces of class ${\rm VII}_0$

Dloussky¹,

Oeljeklaus²

1999

Annales De L’institut Fourier

View full text Add to dashboard Cite

“…In particular, they may serve as a complementary tool for the classification of foliations on surfaces (see [3] for that of non-singular foliations and [4] for an account on the singular case).…”

Section: Introductionmentioning

confidence: 99%

Sections with isolated singularities

Campillo

Olivares

2003

Mathematical Research Letters

View full text Add to dashboard Cite

Abstract. Let E −→ M be a holomorphic rank n vector bundle over a compact Kähler manifold of dimension n, having a positive (or ample) line bundle L −→ M and consider a global section s, with isolated singularities, of the twisted bundle E ⊗ L ⊗r , where r is an integer.We prove that if r is large enough, then s is uniquely determined, up to a global endomorphism of the bundle E, by its subscheme of singular points (which we call the singular subscheme of s).If in particular E is simple, then s is uniquely determined, up to a scalar factor, by its singular subscheme.We recall that the last statement holds in case s is a holomorphic foliation by curves, with isolated singularities, on a projective manifold M with stable tangent bundle, so it holds in particular if M is a compact irreducible Hermitian symmetric space or a Calabi-Yau manifold.If L −→ P n is the hyperplane bundle, we show that it holds for every r ≥ 1.

show abstract

“…Le flot de θ sur S induit alors soit une action effective de (C , ·), soit une action effective de (C, +). Le fait qu'un champ de vecteurs non trivial sur S doit s'annuler (voir par exemple [2]) et le théorème suivant nous montrent que seul le second cas resteàélucider.…”

Section: Introduction Et Rappelsunclassified

Surfaces de la classe VII0 admettant un champ de vecteurs

Dloussky

Oeljeklaus

Toma³

2000

Comment. Math. Helv.

View full text Add to dashboard Cite

Résumé. Nous montrons qu'une surface de la classe VII 0 avec b 2 > 0 sur laquelle existe un champ de vecteurs non trivial contient exactement b 2 courbes rationnelles. Il s'ensuit par un théorème de I. Nakamura qu'une telle surface se déforme en une surface de Hopf primairé eclatée. Ce résultat contribueà la classification des surfaces complexes compactes avec champs de vecteurs.Abstract. We prove that a compact complex surface of class VII 0 with b 2 > 0 admitting a non trivial holomorphic vector field contains exactly b 2 rational curves. A theorem of I. Nakamura then implies that such a surface is a deformation of a blown-up primary Hopf surface. This result contributes to the classification of compact complex surfaces with holomorphic vector fields. Mathematics Subject Classification (2000). 32J15, 32L30, 32M05, 57R30.

show abstract

Feuilletages holomorphes sur les surfaces complexes compactes

Cited by 72 publications

References 15 publications

Vector fields and foliations on compact surfaces of class ${\rm VII}_0$

Vector fields and foliations on compact surfaces of class ${\rm VII}_0$

Sections with isolated singularities

Surfaces de la classe VII0 admettant un champ de vecteurs

Contact Info

Product

Resources

About