# Some Recent Transcendental Techniques in Algebraic and Complex Geometry

 Title: Some Recent Transcendental Techniques in Algebraic and Complex Geometry Author: Siu, Yum-Tong Citation: 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. Full Text & Related Files: siu_icm2002_talk.pdf (235.4Kb; PDF) 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. Published Version: http://www.mathunion.org/ICM/ICM2002.1/ICM2002.1.ocr.pdf Other Sources: https://arxiv.org/abs/math/0212402 Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:32192700 Downloads of this work: