These notes are an expanded version of lectures delivered at the AMS Summer School on
Algebraic Geometry, held at Santa Cruz in July 1995. The main goal of the notes is to study …

The origin of Nevanlinna theory comes from the fundamental theorem of algebra which says
that every complex polynomial equation P (z)= 0 has d number of roots counting …

Diophantine Approximation and Nevanlinna Theory Page 1 Diophantine Approximation and
Nevanlinna Theory Paul Vojta 1 Introduction Beginning with the work of Osgood [65], it has …

The study of entire holomorphic curves contained in projective algebraic varieties is
intimately related to fascinating questions of geometry and number theory—especially …

We establish the second main theorem with the best truncation level one for the k-jet lift Jk
(ƒ):→ Jk (A) of an algebraically non-degenerate entire holomorphic curve ƒ:→ A into a semi …

approximation” method, which was soon recognized to be an important tool in the study of
holomorphic foliations, in parallel with Nevanlinna theory and the construction of Ahlfors …

Let f: C-+ A be an entire holomorphic curve from the complex plane C into a semi-Abelian
variety A. It was proved by [No2] that the Zariski closure of f (C) is a translate of a semi …

We deal with the distributions of holomorphic curves and integral points off divisors. We will
simultaneously prove an optimal dimension estimate from above of a subvariety W off a …

Hyperbolic complex manifolds have been studied extensively during the last 30 years (see,
for example,[10],[11]). However, it is still an important problem in hyperbolic geometry to …

The purpose of this paper is to prove the following: If the image of a holomorphic map f from
C to an Abelian variety A is Zariski dense, then the counting function with respect to f and a …