## Asian Journal of Mathematics

### Essentially Large Divisors and their Arithmetic and Function-theoretic Inequalities

#### Abstract

Motivated by the classical Theorems of Picard and Siegel and their generalizations, we define the notion of an essentially large effective divisor and derive some of its arithmetic and function-theoretic consequences. We then investigate necessary and sufficient criteria for divisors to be essentially large. In essence, we prove that on a nonsingular irreducible projective variety $X$ with $\mathrm{Pic}(X) = \mathbb{Z}$, every effective divisor with $\operatorname{dim}X + 2$ or more components in general position is essentially large.

#### Article information

Source
Asian J. Math., Volume 16, Number 3 (2012), 387-408.

Dates
First available in Project Euclid: 23 November 2012