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YCor
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Two different complex manifolds with the same cohomology

Is there an example of two non-homeomorphic projective smooth complex varieties $X$ and $Y$ such that there exists an isomorphism $H^{\ast}(X,\mathbb{C})\rightarrow H^{\ast}(Y,\mathbb{C})$ of commutative-graded algebras compatible with Hodge filtration.