Some recent transcendental techniques in algebraic and complex geometry

2002/12/01 by Yum-Tong Siu · 1 citation
Mathematics · #math.CV #math.AG #msc:20C30 #msc:20J05

paper · pdf

published as Proceedings of the ICM, Beijing 2002, vol. 1, 439--448

arxiv created 2002/12/01 · arxiv updated 2009/12/01

Abstract

This article discusses the recent transcendental techniques used in the proofs of the following three conjectures. (1)~The plurigenera of a compact projective algebraic manifold are invariant under holomorphic deformation. (2)~There exists no smooth Leviflat hypersurface in the complex projective plane. (3)~A generic hypersurface of sufficiently high degree in the complex projective space is hyperbolic in the sense that there is no nonconstant holomorphic map from the complex Euclidean line to it.

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