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 …

An English translation of a book that first appeared in Japanese. It provides an account of
recent developments in geometric function theory in several complex variables and presents …

This paper proves a finiteness result for families of integral points on a semiabelian variety
minus a divisor, generalizing the corresponding result of Faltings for abelian varieties …

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 …

It is shown that if n∈ ℕ, c∈ ℂ n, and three distinct values of a meromorphic function f: ℂ n sr
1 of hyper-order gV (f) strictly less than 2/3 have forward invariant pre-images with respect to …

We prove new theorems that are higher-dimensional generalizations of the classical
theorems of Siegel on integral points on affine curves and of Picard on holomorphic maps …

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

Given a complex quasi-projective normal variety $ X $ and a linear representation
$\varrho:\pi_1 (X)\to {\rm GL} _ {N}(K) $ with $ K $ any field of positive characteristic, we …

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 …