# nLab complex geometry

complex geometry

### Examples

#### Analytic geometry

analytic geometry (complex, rigid, global)

## Basic concepts

analytic function

analytification

## Theorems

GAGA

#### Differential geometry

differential geometry

synthetic differential geometry

# Contents

## Idea

In complex geometry one studies complex manifolds as a special case of how in general differential geometry one studies more generally smooth manifolds.

In complex analytic geometry one studies, more generally, complex analytic spaces.

## Properties

### GAGA principle and relation to algebraic geometry

complex analytic geometry is closely related to algebraic geometry over the complex numbers. See at GAGA for more on this.

## References

• Daniel Huybrechts Complex geometry - an introduction. Springer (2004). Universitext. 309 pages. (pdf)

Revised on August 10, 2014 06:29:13 by Urs Schreiber (185.37.147.14)