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We will cover the basics of several complex variables in 4 lectures: Basic properties of holomorphic functions in several variables, the notion of pseudoconvexity, CR functions and CR geometry, and the \(\bar \partial \) -problem. The main underlying idea is to connect various characterizations of domains of holomorphy, that is, the natural domains of definition for holomorphic functions. In the process we will connect the function theory on the domain to geometric properties of the boundary, and discuss the relationship between the boundary values and the functions themselves and extension of holomorphic functions from subspaces. These lecture notes roughly correspond to the first 4 chapters of the book of the same name (J. Lebl [1], Tasty bits of several complex variables Independently published: https://www.jirka.org/scv/ , (2023)).

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Tasty Bits of Several Complex Variables

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  • 发表日期：

    2025年

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  • Sean Curry,
  • Jiří Lebl

摘要

We will cover the basics of several complex variables in 4 lectures: Basic properties of holomorphic functions in several variables, the notion of pseudoconvexity, CR functions and CR geometry, and the \(\bar \partial \) -problem. The main underlying idea is to connect various characterizations of domains of holomorphy, that is, the natural domains of definition for holomorphic functions. In the process we will connect the function theory on the domain to geometric properties of the boundary, and discuss the relationship between the boundary values and the functions themselves and extension of holomorphic functions from subspaces. These lecture notes roughly correspond to the first 4 chapters of the book of the same name (J. Lebl [1], Tasty bits of several complex variables Independently published: https://www.jirka.org/scv/ , (2023)).