Transcription of Complex Analytic and Differential Geometry
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Complex Analytic and Differential Geometry
Complex Analytic andDifferential GeometryJean-Pierre DemaillyUniversit e de Grenoble IInstitut Fourier, UMR 5582 du CNRS38402 Saint-Martin d H`eres, FranceVersion of Thursday June 21, 20123 Table of ContentsChapter I. Complex Differential Calculus and Differential Calculus on Currents on Differentiable Holomorphic Functions and Complex Subharmonic Plurisubharmonic Domains of Holomorphy and Stein Pseudoconvex Open Sets II. Coherent Sheaves and Analytic Presheaves and The Local Ring of Germs of Analytic Coherent Complex Analytic Sets. Local Complex Analytic Cycles and Meromorphic Normal Spaces and Holomorphic Mappings and Extension Complex Analytic Bimeromorphic maps, Modifications and III. Positive Currents and Lelong Basic Concepts of Closed Positive Definition of Monge-Amp`ere Case of Unbounded Plurisubharmonic Generalized Lelong The Jensen-Lelong Comparison Theorems for Lelong Siu s Semicontinuity Transformation of Lelong Numbers by Direct A Schwarz Lemma.
8 Chapter I. Complex Differential Calculus and Pseudoconvexity M Uα Uα∩Uβ Uβ τβ τα Rm Vα Vβ τα(Uα∩Uβ) τβ(Uα∩Uβ) ταβ Fig. I-1 Charts and transition maps s(Ω,R) the set of functions fof class C son Ω, i.e. such that f τ−1 α; if Ω is not open, Cs(Ω,R) is the set of functions which have a Csextension to some neighborhood of Ω.
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