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Special Varieties and Classification Theory: An Overview

Special Varieties and Classification Theory: An Overview Lang's conjectures link the geometric, hyperbolic, and arithmetic properties of projective complex varieties of general type. We propose here an extension of these conjectures to arbitrary projective varieties X. This extension rests on the notion of ‘special’ variety. This class contains manifolds either rationally connected or with vanishing Kodaira dimension. We further construct for any X its ‘core’, which is a fibration c X : X→C(X) with general fibre special and orbifold base of general type. This fibration seems to permit us to decompose X according to the dichotomy ‘special’ vs ‘general type’, and not only leads to the above-mentioned extension of Lang's conjectures but also to a simple global view of classification theory. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Special Varieties and Classification Theory: An Overview

Acta Applicandae Mathematicae , Volume 75 (3) – Oct 5, 2004

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References (28)

Publisher
Springer Journals
Copyright
Copyright © 2003 by Kluwer Academic Publishers
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1023/A:1022367408092
Publisher site
See Article on Publisher Site

Abstract

Lang's conjectures link the geometric, hyperbolic, and arithmetic properties of projective complex varieties of general type. We propose here an extension of these conjectures to arbitrary projective varieties X. This extension rests on the notion of ‘special’ variety. This class contains manifolds either rationally connected or with vanishing Kodaira dimension. We further construct for any X its ‘core’, which is a fibration c X : X→C(X) with general fibre special and orbifold base of general type. This fibration seems to permit us to decompose X according to the dichotomy ‘special’ vs ‘general type’, and not only leads to the above-mentioned extension of Lang's conjectures but also to a simple global view of classification theory.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Oct 5, 2004

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