Asian Journal of Mathematics

Essentially Large Divisors and their Arithmetic and Function-theoretic Inequalities

Gordon Heier and Min Ru

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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

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1353696013

Mathematical Reviews number (MathSciNet)
MR2989226

Zentralblatt MATH identifier
1320.11058

Subjects
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}

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

Citation

Heier, Gordon; Ru, Min. Essentially Large Divisors and their Arithmetic and Function-theoretic Inequalities. Asian J. Math. 16 (2012), no. 3, 387--408. https://projecteuclid.org/euclid.ajm/1353696013


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