complex geometry

# Contents

## Definition

A biholomorphic function is a holomorphic function which is a bijection on the underlying sets and whose set-theoretic inverse is also holomorphic.

## Properties

If $f:U\to V$ is a bijective holomorphic map of open subsets of complexfied Cartesian space ${\mathbb{C}}^n$, then the determinant of the Jacobian $J(f)$ is nowhere $0$, that is $f^{-1}$ is holomorphic.

(See this MO discussion and also this other MO discussion)

## References

• Eric Bedford, What is… a Biholomorphic Mapping, Notices of the AMS,volume 59, number 6 (pdf)

Last revised on July 19, 2014 at 20:49:23. See the history of this page for a list of all contributions to it.