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# Asian Journal of Mathematics

## Volume 16 (2012)

### Number 3

### Essentially large divisors and their arithmetic and function-theoretic inequalities

Pages: 387 – 407

DOI: http://dx.doi.org/10.4310/AJM.2012.v16.n3.a2

#### Authors

#### Abstract

otivated 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 Pic(X) = Z, every effective divisor with dimX + 2 or more components in general position is essentially large.

#### Keywords

Integral points, entire curves, hyperbolicity, Weil functions, Schmidt Subspace Theorem, Second Main Theorem

#### 2010 Mathematics Subject Classification

11G35, 11G50, 14C20, 14G40, 32H30