On essentially large divisors

Details On essentially large divisors On essentially large divisors

2010-06-07

arxiv.org/abs/1006.1306v1

Mathematics

Algebraic Geometry

20 pages

Scientific paper

Motivated by the classical Theorems of Picard and Siegel and their generalizations, we define the notion of an {\it essentially large} effective divisor and derive some of its geometric and arithmetic consequences. We then prove that on a nonsingular projective variety $X$ whose codimension is no greater than $\dim X-2$, every effective divisor with $\dim X +2$ or more components in general position is essentially large.

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