Extension of germs of holomorphic foliations
نویسندگان
چکیده
منابع مشابه
Rigidity of Certain Holomorphic Foliations
There is a well-known rigidity theorem of Y. Ilyashenko for (singular) holomorphic foliations in CP and also the extension given by Gómez-Mont and Ort́ız-Bobadilla (1989). Here we present a different generalization of the result of Ilyashenko: some cohomological and (generic) dynamical conditions on a foliation F on a fibred complex surface imply the d-rigidity of F , i.e. any topologically triv...
متن کاملLimits in differential fields of holomorphic germs
Differential fields of germs of continuous real valued functions of one real variable (Hardy fields) have the property that all elements have limits in the extended real numbers and thus have a canonical valuation. For differential fields of holomorphic germs this is not generally the case. We provide a criterion for differential fields of holomorphic germs for its elements to have uniform limi...
متن کاملHolomorphic Dynamics near Germs of Singular Curves
Let M be a two dimensional complex manifold, p ∈ M and F a germ of holomorphic foliation of M at p. Let S ⊂ M be a germ of an irreducible, possibly singular, curve at p in M which is a separatrix for F . We prove that if the Camacho-Sad-Suwa index Ind(F , S, p) 6∈ Q ∪ {0} then there exists another separatrix for F at p. A similar result is proved for the existence of parabolic curves for germs ...
متن کاملAbelian integrals in holomorphic foliations
The aim of this paper is to introduce the theory of Abelian integrals for holomorphic foliations in a complex manifold of dimension two. We will show the importance of Picard-Lefschetz theory and the classification of relatively exact 1-forms in this theory. As an application we identify some irreducible components of the space of holomorphic foliations of a fixed degree and with a center singu...
متن کاملCommuting holonomies and rigidity of holomorphic foliations
In this article we study deformations of a holomorphic foliation with a generic non-rational first integral in the complex plane. We consider two vanishing cycles in a regular fiber of the first integral with a non-zero self intersection and with vanishing paths which intersect each other only at their start points. It is proved that if the deformed holonomies of such vanishing cycles commute t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales de la faculté des sciences de Toulouse Mathématiques
سال: 2015
ISSN: 0240-2963,2258-7519
DOI: 10.5802/afst.1455