Browsing by Author "Siu, YumTong"
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Abundance Conjecture
Siu, YumTong (International Press, 2010)We sketch a proof of the abundance conjecture that the Kodaira dimension of a compact complex algebraic manifold equals its numerical Kodaira dimension. The proof consists of the following three parts: (i) the case of ... 
Dynamic Multiplier Ideal Sheaves and the Construction of Rational Curves in Fano Manifolds
Siu, YumTong (Uppsala Universitet. Acta Universitatis Upsaliensis, 2009) 
Holomorphically parametrized L2 Cramer's rule and its algebraic geometric applications
Sung, Yih (20131008)Suppose $f,g_1,\cdots,g_p$ are holomorphic functions over $\Omega\subset\cxC^n$. Then there raises a natural question: when can we find holomorphic functions $h_1,\cdots,h_p$ such that $f=\sum g_jh_j$? The celebrated Skoda ... 
Hyperbolicity of generic highdegree hypersurfaces in complex projective space
Siu, YumTong (Springer Science + Business Media, 2015) 
Some Recent Transcendental Techniques in Algebraic and Complex Geometry
Siu, YumTong (International Congress of Mathematicians, 2002)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. ... 
Techniques for the Analytic Proof of the Finite Generation of the Canonical Ring
Siu, YumTong (International Press of Boston, 2009)This article is written for the Proceedings of the Conference on Current Developments in Mathematics in Harvard University, November 1617, 2007. It is an exposition of the analytic proof of the finite generation of the ...