Hodge variety

From Encyclopedia of Mathematics
Jump to: navigation, search

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.


[1] P.A. Griffiths, J.E. Harris, "Principles of algebraic geometry" , 1 , Wiley (1978) MR0507725 Zbl 0408.14001
How to Cite This Entry:
Hodge variety. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.L. Onishchik (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article