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

Essentially large divisors and their arithmetic and function-theoretic inequalities