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A geometric description of Hazama's exceptional classes

Federica Galluzzi (2000)

Bollettino dell'Unione Matematica Italiana

Sia X una varietà abeliana complessa di tipo Mumford. In queste note daremo una descrizione esplicita delle classi eccezionali in B 2 X × X trovate da Hazama in [Ha] e le descriveremo geometricamente usando la grassmaniana delle rette di P 7 .

Équidistribution des sous-variétés de petite hauteur

Pascal Autissier (2006)

Journal de Théorie des Nombres de Bordeaux

On montre dans cet article que le théorème d’équidistribution de Szpiro-Ullmo-Zhang concernant les suites de petits points sur les variétés abéliennes s’étend au cas des suites de sous-variétés. On donne également une version quantitative de ce résultat.

Galois orbits and equidistribution: Manin-Mumford and André-Oort.

Andrei Yafaev (2009)

Journal de Théorie des Nombres de Bordeaux

We overview a unified approach to the André-Oort and Manin-Mumford conjectures based on a combination of Galois-theoretic and ergodic techniques. This paper is based on recent work of Klingler, Ullmo and Yafaev on the André-Oort conjecture, and of Ratazzi and Ullmo on the Manin-Mumford conjecture.

Isogeny orbits in a family of abelian varieties

Qian Lin, Ming-Xi Wang (2015)

Acta Arithmetica

We prove that if a curve of a nonisotrivial family of abelian varieties over a curve contains infinitely many isogeny orbits of a finitely generated subgroup of a simple abelian variety, then it is either torsion or contained in a fiber. This result fits into the context of the Zilber-Pink conjecture. Moreover, by using the polyhedral reduction theory we give a new proof of a result of Bertrand.

Logarithmic Surfaces and Hyperbolicity

Gerd Dethloff, Steven S.-Y. Lu (2007)

Annales de l’institut Fourier

In 1981 J. Noguchi proved that in a logarithmic algebraic manifold, having logarithmic irregularity strictly bigger than its dimension, any entire curve is algebraically degenerate.In the present paper we are interested in the case of manifolds having logarithmic irregularity equal to its dimension. We restrict our attention to Brody curves, for which we resolve the problem completely in dimension 2: in a logarithmic surface with logarithmic irregularity 2 and logarithmic Kodaira dimension 2 , any...

On Brody and entire curves

Jörg Winkelmann (2007)

Bulletin de la Société Mathématique de France

We discuss an example of an open subset of a torus which admits a dense entire curve, but no dense Brody curve.

On coverings of simple abelian varieties

Olivier Debarre (2006)

Bulletin de la Société Mathématique de France

To any finite covering f : Y X of degree d between smooth complex projective manifolds, one associates a vector bundle E f of rank d - 1 on X whose total space contains Y . It is known that E f is ample when X is a projective space ([Lazarsfeld 1980]), a Grassmannian ([Manivel 1997]), or a Lagrangian Grassmannian ([Kim Maniel 1999]). We show an analogous result when X is a simple abelian variety and f does not factor through any nontrivial isogeny X ' X . This result is obtained by showing that E f is M -regular in the...

The optimality of the Bounded Height Conjecture

Evelina Viada (2009)

Journal de Théorie des Nombres de Bordeaux

In this article we show that the Bounded Height Conjecture is optimal in the sense that, if V is an irreducible subvariety with empty deprived set in a power of an elliptic curve, then every open subset of V does not have bounded height. The Bounded Height Conjecture is known to hold. We also present some examples and remarks.

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