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For questions about or involving complex manifolds.
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Are induced morphisms on cohomology strict with respect to the hodge filtration in the non K...
The following is a counterexample of what you ask for non-compact Kähler manifolds.
Let $X$ be a smooth projective variety and $D \subset X$ a very ample divisor. Since $U:= X- D$ is affine, the filt …