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VOL. 2003 | 2004 On some problems of Kobayashi and Lang; algebraic approaches
Claire Voisin

Editor(s) A.J. de Jong, David Jerison, George Lusztig, Barry Mazur, Wilfried Schmid, Shing-Tung Yau

Abstract

The goal of this survey paper is to present results on hyperbolicity of complex algebraic manifolds, which appeared after the papers [48] and [42], where a number of important and intriguing conjectures were proposed. Since the paper puts the accent on measure hyperbolicity on one hand, and on algebraic methods on the other hands, we hope it will not overlap too much with the beautiful paper [21] by Demailly, except for the basic definitions and starting points. The basic questions asked in [42], and in a different spirit in [48] concern the relationships between curvature properties of a given complex manifold (or complex algebraic variety) on one hand, and the behaviour of holomorphic maps from disks or polydisks to them, on the other hand, or, from a more algebraic point of view, the (non) existence of subvarieties of certain types.

Information

Published: 1 January 2004
First available in Project Euclid: 14 June 2005

zbMATH: 1215.32014
MathSciNet: MR2132645

Rights: Copyright © 2004 International Press of Boston

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