Is there a holomorphic diffeomorphism $f:\mathbb{C}P^{2n+1}\to \mathbb{C}P^{2n+1}$ without fixed point?
2026-03-26 04:51:44.1774500704
Is there a holomorphic diffeomorphism of $\mathbb{C}P^{2n+1}$ without fixed point?
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No. The holomorphic diffeomorphisms of $\mathbb C P^n$ are $PGL_{n+1}$. These always have fixed points because every matrix has an eigenvector.