# Hodge variety

From Encyclopedia of Mathematics

*Hodge manifold*

A complex manifold on which a Hodge metric can be given, that is, a Kähler metric whose fundamental form defines an integral cohomology class. A compact complex manifold is a Hodge manifold if and only if it is isomorphic to a smooth algebraic subvariety of some complex projective space (Kodaira's projective imbedding theorem).

See also Kähler manifold.

#### References

[1] | P.A. Griffiths, J.E. Harris, "Principles of algebraic geometry" , 1 , Wiley (1978) |

**How to Cite This Entry:**

Hodge variety.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Hodge_variety&oldid=12390

This article was adapted from an original article by A.L. Onishchik (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article