Having a complex projective variety $X=\bigcup_{\alpha \in A} X_\alpha$, where $X_\alpha$ are its irreducible components, is it true that an arbitrary biholomorphic map $\phi:X\rightarrow X$ sends its irreducible components to irreducible components (in some permutation of the set $A$)?
2026-03-31 10:14:46.1774952086
Biholomorphism of a projective variety preserves the set of irreducible components
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