This paper establishes a hypersurface defect relation, that is, , for a family of meromorphic maps from a generalized p-parabolic manifold M to the projective space ℙⁿ, under some weak non-degeneracy assumptions.
We consider a nondegenerate holomorphic map where is a compact Hermitian manifold of dimension larger than or equal to and is an open connected complex manifold of dimension . In this article we give criteria which permit to construct Ahlfors’ currents in .
We study algebraic dependences of three meromorphic mappings which share few moving hyperplanes without counting multiplicity.
In this paper, the definition of the derivative of meromorphic functions is extended to holomorphic maps from a plane domain into the complex projective space. We then use it to study the normality criteria for families of holomorphic maps. The results obtained generalize and improve Schwick's theorem for normal families.
On a finite intersection of strictly pseudoconvex domains we define two kinds of natural Nevanlinna classes in order to take the growth of the functions near the sides or the edges into account. We give a sufficient Blaschke type condition on an analytic set for being the zero set of a function in a given Nevanlinna class. On the other hand we show that the usual Blaschke condition is not necessary here.
We determine which algebraic surface of logarithmic irregularity admit an algebraically non-degenerate entire curve.
We use orbifold structures to deduce degeneracy statements for holomorphic maps into logarithmic surfaces. We improve former results in the smooth case and generalize them to singular pairs. In particular, we give applications on nodal surfaces and complements of singular plane curves.
Nous construisons pour toute correspondance polynomiale d’exposant de Lojasiewicz une mesure d’équilibre . Nous montrons que est approximable par les préimages d’un point générique et que les points périodiques répulsifs sont équidistribués sur le support de . En utilisant ces résultats, nous donnons une caractérisation des ensembles d’unicité pour les polynômes.
We determine the asymptotics of the joint eigenfunctions of the torus action on a toric Kähler variety. Such varieties are models of completely integrable systems in complex geometry. We first determine the pointwise asymptotics of the eigenfunctions, which show that they behave like Gaussians centered at the corresponding classical torus. We then show that there is a universal Gaussian scaling limit of the distribution function near its center. We also determine the limit...
This paper deals with the finiteness problem of meromorphic funtions on an annulus sharing four values regardless of multiplicity. We prove that if three admissible meromorphic functions , , on an annulus share four distinct values regardless of multiplicity and have the complete identity set of positive counting function, then or or . This result deduces that there are at most two admissible meromorphic functions on an annulus sharing a value with multiplicity truncated to level and...
We prove some finiteness theorems for differential nondegenerate meromorphic mappings of into ℙⁿ(ℂ) which share n+3 hyperplanes.
The purpose of this article is twofold. The first is to find the dimension of the set of integral points off divisors in subgeneral position in a projective algebraic variety , where k is a number field. As consequences, the results of Ru-Wong (1991), Ru (1993), Noguchi-Winkelmann (2003) and Levin (2008) are recovered. The second is to show the complete hyperbolicity of the complement of divisors in subgeneral position in a projective algebraic variety