Several Complex Variables
Domains of holomorphy, Stein manifolds, and the Cauchy–Fantappiè formula.
Several Complex Variables. Domains of holomorphy, Stein manifolds, and the Cauchy–Fantappiè formula.
Foundations and canonical references
The standard treatments of several complex variables approach the subject from complementary angles. Hormander, An Introduction to Complex Analysis in Several Variables (1990) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Fritzsche, From Holomorphic Functions to Complex Manifolds (2002) offers an alternative presentation that complements the primary references and is useful for triangulating definitions and proof techniques.
Open methodological questions for several complex variables include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1990An Introduction to Complex Analysis in Several Variableshormander-1990
- textbook · supporting · 2002From Holomorphic Functions to Complex Manifoldsfritzsche-2002, grauert-2002
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