Browsing by Author "Siu, Yum-Tong"
Now showing items 1-12 of 12
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Abundance Conjecture
Siu, Yum-Tong (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, Yum-Tong (Uppsala Universitet. Acta Universitatis Upsaliensis, 2009) -
An Effective Matsusaka Big Theorem
Siu, Yum-Tong (Cellule MathDoc/CEDRAM, 1993)We prove the following effective form of Matsusaka's Big Theorem. For an ample line bundle L over a compact complex manifold X of complex dimension n with canonical line bundle K(X), the line bundle mL is very ample for m ... -
Holomorphically parametrized L2 Cramer's rule and its algebraic geometric applications
Sung, Yih (2013-10-08)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 high-degree hypersurfaces in complex projective space
Siu, Yum-Tong (Springer Science + Business Media, 2015) -
Invariance of Plurigenera and Torsion-Freeness of Direct Image Sheaves of Pluricanonial Bundles
Siu, Yum-TongThe deformational invariance of plurigenera proved recently by the author is a special case of the torsion-free property of the first direct image sheaf of the pluricanonical line bundle when the target space of the proper ... -
New Procedure to Generate Multipliers in Complex Neumann Problem and Effective Kohn Algorithm
Siu, Yum-Tong (Springer Nature, 2017-04-26)The purpose of this paper is threefold. (i) To explain the effective Kohn algorithm for multipliers in the complex Neumann problem and its difference with the full-real-radical Kohn algorithm, especially in the context of ... -
Nonexistence of Smooth Levi-Flat Hypersurfaces in Complex Projective Spaces of Dimension ≥ 3
Siu, Yum-Tong (2000-05) -
Some Recent Transcendental Techniques in Algebraic and Complex Geometry
Siu, Yum-Tong (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, Yum-Tong (International Press of Boston, 2009)This article is written for the Proceedings of the Conference on Current Developments in Mathematics in Harvard University, November 16-17, 2007. It is an exposition of the analytic proof of the finite generation of the ... -
Very Ampleness Part of Fujita’s Conjecture and Multiplier Ideal Sheaves of Kohn and Nadel
Siu, Yum-Tong (2001)