Several Complex Variables

The theory of holomorphic functions in several complex variables is one of the cornerstones of 20th century mathematics. Far from being a simple generalisation of single-variable complex analysis, the development of this theory requires the modern viewpoint of homological algebra and sheaf theory.

These notes are adapted and expanded from the topics course MA4291 Several Complex Variables, offered in AY2018/19 Semester 1 by Prof Chin Chee Whye. The main text for this course is J. L. Taylor, Several Complex Variables with Connections to Algebraic Geometry and Lie Groups (2002).

• Several Complex Variables (I): $z$ and $\overline z$
• Several Complex Variables (II): Holomorphic functions
• Several Complex Variables (III): Hartogs's Phenomenon
• Several Complex Variables (IV): Domains of Holomorphy
• Several Complex Variables (V): Local Behaviour
• Several Complex Variables (VI): Implicit Mapping Theorem
• Several Complex Variables (VII): The Local Ring of Germs
• Several Complex Variables (VIII): Varieties in $\bb C^n$

(In progress, last updated 18 Sep 2018)