For smooth projective X/ℂ: Hᵏ(X,ℂ) = ⊕_{p+q=k} H^{p,q}(X). Hodge structures, polarised variations, period map. Deligne's mixed Hodge structures.
For smooth projective X/ℂ: Hᵏ(X,ℂ) = ⊕_{p+q=k} H^{p,q}(X). Hodge structures, polarised variations, period map. Deligne's mixed Hodge structures.