Related papers: On Holomorphic Curves in Semi-Abelian Varieties

Applying the Second Main Theorem we deal with the algebraic degeneracy of entire holomorphic curves from the complex plane into a complex algebraic normal variety of positive log Kodaira dimension that admits a finite proper morphism to a…

In [Ann. of Math. 169 (2009)], Min Ru proved a second main theorem for algebraically nondegenerate holomorphic curves in complex projective varieties intersecting fixed hypersurface targets. In this paper, by introducing a new proof method…

We establish the second main theorem with the best truncation level one for an entire holomorphic curve $f:\C \to A$ into a semi-abelian variety $A$ and an arbitrary effective reduced divisor $D$ on $A$; the low truncation level is…

In this paper, we prove a lemma on logarithmic derivative for holomorphic curves from annuli into K\"{a}hler compact manifold and. As its application, a second main theorem for holomophic curves from annuli into semi abelian varieties…

The study of entire holomorphic curves contained in projective algebraic varieties is intimately related to fascinating questions of geometry and number theory -- especially through the concepts of curvature and positivity which are central…

We prove a product decomposition of the Zariski closure of the jet lifts of a holomorphic map f from C into a semi-abelian variety A, provided that f is of finite order. On the other hand, by giving an example of such a map f into a three…

We consider the algebraic degeneracy of holomorphic curves from a point of view of meromorphic vector fields. Employing the notion of Jocabian sections introduced by W. Stoll, we establish a Second Main Theorem type inequality. As…

Towards the Lang--Vojta conjecture, we prove results on finiteness and Zariski degeneracy of $S$-integral points of varieties over number fields $k$, including many cases with geometrically irreducible boundary divisors. Our approach builds…

Let f:C -> A be an entire holomorphic curve into a semi-Abelian variety A. Then the Zariski closure of f(C) is a translate of a semi-Abelian subvariety of A (logarithmic Bloch-Ochiai's theorem). The purpose of the present paper is to…

We prove a boundedness-theorem for families of abelian varieties with real multiplication. More generally, we study curves in Hilbert modular varieties from the point of view of the Green Griffiths-Lang conjecture claiming that entire…

We introduce the separating semigroup of a real algebraic curve of dividing type. The elements of this semigroup record the possible degrees of the covering maps obtained by restricting separating morphisms to the real part of the curve. We…

We associate Hamiltonian homological evolutionary vector fields --which are the non-Abelian variational Lie algebroids' differentials-- with Lie algebra-valued zero-curvature representations for partial differential equations.

We investigate the problem of holomorphic algebraizibility for real hypersurfaces in complex space. We introduce a new invariant of a (real-analytic) Levi-nondegenerate hypersurface called {\em the jet transcendence degree}. Using this…

In this paper, we prove the geometric Bombieri-Lang conjecture for projective varieties which have finite morphisms to abelian varieties of trivial traces over function fields of characteristic 0. The proof is based on the idea of…

{Let $K$ be a number field, and $A_1,A_2$ abelian varieties over $K$. Let $P$ (resp. $Q$) be a non-torsion point in $ A_1(K)$ (resp. $A_2(K)$) such that for almost all places $v$ of $K$, the order of $Q$ mod $v$ divides the order of $P$ mod…

Severi varieties and Brill-Noether theory of curves on K3 surfaces are well understood. Yet, quite little is known for curves on abelian surfaces. Given a general abelian surface $S$ with polarization $L$ of type $(1,n)$, we prove…

We extend Atiyah's holomorphic jet bundle formalism to holomorphic vector bundles over noncommutative algebras endowed with a bigraded differential calculus truncated at bidegree $(1,1)$; we refer to such structures as noncommutative…

A remarkable result of Peter O'Sullivan asserts that the algebra epimorphism from the rational Chow ring of an abelian variety to its rational Chow ring modulo numerical equivalence admits a (canonical) section. Motivated by Beauville's…

In this work, it is established that for a generic projective hypersurface $H\subset\mathbb{P}^n(\mathbb{C})$ of degree $d\geq(5n)^2\,n^{n}$, any holomorphic entire curve $f\colon\mathbb{C}\to\mathbb{P}^n(\mathbb{C})\setminus H$ has its…

The class-invariant homomorphism allows one to measure the Galois module structure of extensions obtained by dividing points on abelian varieties. In this paper, we consider the case when the abelian variety is the Jacobian of a Fermat…