Here is a version of $\partial\bar{\partial}$-lemma from Voisin's book.
I'm confused. If we take $f$ to be any smooth function on $X$ and set $\omega=df$, doesn't the proposition imply that $\omega$ has to be zero? Am I missing something?
2026-03-27 18:07:04.1774634824
Doubt about $\partial\bar{\partial}$-lemma
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