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Название: Complex Analytic and Differential Geometry
Автор: Demailly J.-P.
This introductive chapter is mainly a review of the basic tools and concepts which will be employed in the rest of the book: differential forms, currents, holomorphic and plurisubharmonic functions, holomorphic convexity and pseudoconvexity. Our study of holomorphic convexity is principally concentrated here on the case of domains in Cn. The more powerful machinery needed for the study of general complex varieties (sheaves, positive currents, hermitian differential geometry) will be introduced in Chapters II to V. Although our exposition pretends to be almost self-contained, the reader is assumed to have at least a vague familiarity with a few basic topics, such as differential calculus, measure theory and distributions, holomorphic functions of one complex variable, . . . . Most of the necessary background can be found in the books of [Rudin 1966] and [Warner 1971]; the basics of distribution theory can be found in Chapter I of [H¨ormander 1963]. On the other hand, the reader who has already some knowledge of complex analysis in several variables should probably bypass this chapter.