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Regularization of closed positive currents and Intersection Theory
— LetX be a compact complex manifold and let T be a closed positive current of bidegree (1, 1) on X . It is shown that T is the weak limit of a sequence (Tk) of smooth closed real (1, 1)-currentsExpand
Semi-continuity of complex singularity exponents and K\
Abstract We introduce complex singularity exponents of plurisubharmonic functions and prove a general semi-continuity result for them. This concept contains as a special case several similar conceptsExpand
Algebraic criteria for Kobayashi hyperbolic projective varieties and jet differentials
These notes are an expanded version of lectures delivered at the AMS Summer School on Algebraic Geometry, held at Santa Cruz in July 1995. The main goal of the notes is to study complex varietiesExpand
Analytic Methods in Algebraic Geometry
These notes are derived in part from the lectures “Multiplier ideal sheaves and analytic methods in algebraic geometry” given at the ICTP School held in Trieste, Italy, April 24 – May 12, 2000Expand
Numerical characterization of the Kahler cone of a compact Kahler manifold
The goal of this work is to give a precise numerical description of the Kahler cone of a compact Kahler manifold. Our main result states that the Kahler cone depends only on the intersection form ofExpand
The pseudo-effective cone of a compact K\
We prove that a holomorphic line bundle on a projective manifold is pseudo-effective if and only if its degree on any member of a covering family of curves is non-negative. This is a consequence of aExpand
A numerical criterion for very ample line bundles
— Let X be a projective algebraic manifold of dimension n and let L be an ample line bundle over X . We give a numerical criterion ensuring that the adjoint bundle KX + L is very ample. TheExpand
Compact complex manifolds with numerically effective tangent bundles
1. Basic properties of nef line bundles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p. 5 1.A. Nef line bundles . . . . . . . . . . . . . .Expand
Monge-Ampère Operators, Lelong Numbers and Intersection Theory
TLDR
This chapter is a survey article on the theory of Lelong numbers, viewed as a tool for studying intersection theory by complex differential geometry, based in part on earlier works and on Siu’s fundamental work. Expand
L 2 vanishing theorems for positive line bundles and adjunction theory
0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .p. 1 1. Preliminary Material . . . . . . . . . . . . . . . . .Expand
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