This two volume work on Positivity in Algebraic Geometry contains a contemporary account
of a body of work in complex algebraic geometry loosely centered around the theme of …

Pj (x0,..., xN)= 0, j= l,..., m in projective space Plover C, so x0,..., xN are the projective
coordinates. An algebraic set will be called a variety if it is irreducible—that is, the …

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 …

The point of such a preamble is to get us to appreciate why number-theorists are often so
fondly devoted to the study of rational points on algebraic curves, and to sense the more …

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

We introduce a new approach to the geometric Bombieri--Lang conjecture for hyperbolic
varieties in characteristic 0. The main idea is to construct an entire curve on a special fiber of …

We construct a family of fibred threefolds present behaviours that contradict the function field
and analytic analogue of the Weak Specialness Conjecture. We prove our results by …