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.
|||P.A. Griffiths, J.E. Harris, "Principles of algebraic geometry" , 1 , Wiley (1978)|
Hodge variety. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hodge_variety&oldid=12390