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Extension and normality of meromorphic mappings into complex projective varieties

Si Duc Quang (2012)

Annales Polonici Mathematici

The purpose of this article is twofold. The first is to show a criterion for the normality of holomorphic mappings into Abelian varieties; an extension theorem for such mappings is also given. The second is to study the convergence of meromorphic mappings into complex projective varieties. We introduce the concept of d-convergence and give a criterion of d-normality of families of meromorphic mappings.

Hyperbolic measure of maximal entropy for generic rational maps of k

Gabriel Vigny (2014)

Annales de l’institut Fourier

Let f be a dominant rational map of k such that there exists s < k with λ s ( f ) > λ l ( f ) for all l . Under mild hypotheses, we show that, for A outside a pluripolar set of Aut ( k ) , the map f A admits a hyperbolic measure of maximal entropy log λ s ( f ) with explicit bounds on the Lyapunov exponents. In particular, the result is true for polynomial maps hence for the homogeneous extension of f to k + 1 . This provides many examples where non uniform hyperbolic dynamics is established.One of the key tools is to approximate the graph of a meromorphic...

On meromorphic functions with maximal defect sum

Pham Duc Thoan, Le Thanh Tung (2011)

Annales Polonici Mathematici

The purpose of this article is twofold. The first is to give necessary conditions for the maximality of the defect sum. The second is to show that the class of meromorphic functions with maximal defect sum is very thin in the sense that deformations of meromorphic functions with maximal defect sum by small meromorphic functions are not meromorphic functions with maximal defect sum.

On the removable singularities for meromorphic mappings.

Evgeny M. Chirka (1996)

Publicacions Matemàtiques

If E is a closed subset of locally finite Hausdorff (2n-2)-measure on an n-dimensional complex manifold Ω and all the points of E are nonremovable for a meromorphic mapping of Ω E into a compact Kähler manifold, then E is a pure (n-1)-dimensional complex analytic subset of Ω.

Points périodiques d’applications birationnelles de 2

Charles Favre (1998)

Annales de l'institut Fourier

Nous donnons une condition suffisante pour l’existence de points périodiques pour une application birationnelle de 2 . Sous cette hypothèse, une estimation précise du nombre de points périodiques de période fixée est obtenue. Nous donnons une application de ce résultat à l’étude dynamique de ces applications, en calculant explicitement l’auto-intersection de leur courant invariant naturellement associé. Nos résultats reposent essentiellement sur le théorème de Bézout donnant le cardinal de l’intersection...

The Fujiki class and positive degree maps

Gautam Bharali, Indranil Biswas, Mahan Mj (2015)

Complex Manifolds

We show that a map between complex-analytic manifolds, at least one ofwhich is in the Fujiki class, is a biholomorphism under a natural condition on the second cohomologies. We use this to establish that, with mild restrictions, a certain relation of “domination” introduced by Gromov is in fact a partial order.

Uniqueness problem for meromorphic mappings with truncated multiplicities and few targets

Gerd Dethloff, Tran Van Tan (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper, using techniques of value distribution theory, we give a uniqueness theorem for meromorphic mappings of m into P n with truncated multiplicities and “few" targets. We also give a theorem of linear degeneration for such maps with truncated multiplicities and moving targets.

Universal reparametrization of a family of cycles : a new approach to meromorphic equivalence relations

David Mathieu (2000)

Annales de l'institut Fourier

We study analytic families of non-compact cycles, and prove there exists an analytic space of finite dimension, which gives a universal reparametrization of such a family, under some assumptions of regularity. Then we prove an analogous statement for meromorphic families of non-compact cycles. That is a new approach to Grauert’s results about meromorphic equivalence relations.

Weak normal and quasinormal families of holomorphic curves

Si Duc Quang, Dau Hong Quan (2018)

Archivum Mathematicum

In this paper we introduce the notion of weak normal and quasinormal families of holomorphic curves from a domain in into projective spaces. We will prove some criteria for the weak normality and quasinormality of at most a certain order for such families of holomorphic curves.

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