Let $\mathbb{C}^2\rightarrow \mathbb{C}^2$ be a map. If $f$ preserves a non-zero holomorphic 2-form, is $f$ a holomorphic map?
A map $\mathbb{C}^2\rightarrow \mathbb{C}^2$ that preserves a holomorphic 2-form.
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complex-analysis
complex-geometry