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)