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.

Thank you all for your very nice comments, it is helpful. I want to add a question with slightly different hypothesis.

second question: Suppose we have a holomorphic map $f:Y\rightarrow X$ between two smooth projective complex varieties such that the induced map $H^{\ast}(X;\mathbb{Q})\rightarrow H^{\ast}(Y;\mathbb{Q})$ is an isomorphism. Is it true that $f$ is an isomorphism ?