Asian Journal of Mathematics

Essentially Large Divisors and their Arithmetic and Function-theoretic Inequalities

Gordon Heier and Min Ru

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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 $\mathrm{Pic}(X) = \mathbb{Z}$, every effective divisor with $\operatorname{dim}X + 2$ or more components in general position is essentially large.

Article information

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

First available in Project Euclid: 23 November 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11G35: Varieties over global fields [See also 14G25] 11G50: Heights [See also 14G40, 37P30] 14C20: Divisors, linear systems, invertible sheaves 14G40: Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30] 32H30: Value distribution theory in higher dimensions {For function- theoretic properties, see 32A22}

Integral points entire curves hyperbolicity Weil functions Schmidt subspace theorem second main theorem


Heier, Gordon; Ru, Min. Essentially Large Divisors and their Arithmetic and Function-theoretic Inequalities. Asian J. Math. 16 (2012), no. 3, 387--408.

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