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Hodge cycle

In [mathematics] , a ** Hodge cycle ** is a particular kind of [homology class] defined on a [complex] [algebraic variety] * V * , or more generally on a [Kähler manifold] . A homology class * x * in a [homology group]

: * H * ** k **

where

:

defined in [algebraic topology] (as a special case of the [universal coefficient theorem] ). The conventional term Hodge

The importance of Hodge cycles lies primarily in the [Hodge conjecture] , to the effect that Hodge cycles should always be [algebraic cycle] s, for

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