Publication: Some Recent Transcendental Techniques in Algebraic and Complex Geometry
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Date
2002
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International Congress of Mathematicians
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Siu, Yum-Tong. 2002. Some Recent Transcendental Techniques in Algebraic and Complex Geometry. In Proceedings of the International Congress of Mathematicians, Beijing, China, August 20-28, 2002, Volume I: 439-448.
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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 plan. (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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Keywords
Plurigenera, Levi-Flat, Hyperbolicity
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