Now showing items 1-6 of 6

• #### Abundance Conjecture ﻿

(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 ﻿

(Uppsala Universitet. Acta Universitatis Upsaliensis, 2009)
• #### Holomorphically parametrized L2 Cramer's rule and its algebraic geometric applications ﻿

(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 ﻿

(Springer Science + Business Media, 2015)
• #### Some Recent Transcendental Techniques in Algebraic and Complex Geometry ﻿

(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 ﻿

(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 ...