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Is there a holomorphic diffeomorphism of $mathbb{C}P^{2n+1}$ without fixed point?
Is there a holomorphic diffeomorphism $f:mathbb{C}P^{2n+1}to mathbb{C}P^{2n+1}$ without fixed point?
complex-analysis fixed-point-theorems projective-space
asked Nov 20 '18 at 16:03
Ali Taghavi
186329
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Is there a holomorphic diffeomorphism $f:mathbb{C}P^{2n+1}to mathbb{C}P^{2n+1}$ without fixed point?
complex-analysis fixed-point-theorems projective-space
asked Nov 20 '18 at 16:03
Ali Taghavi
186329
add a comment |
Is there a holomorphic diffeomorphism $f:mathbb{C}P^{2n+1}to mathbb{C}P^{2n+1}$ without fixed point?
complex-analysis fixed-point-theorems projective-space
asked Nov 20 '18 at 16:03
Ali Taghavi
186329
Is there a holomorphic diffeomorphism $f:mathbb{C}P^{2n+1}to mathbb{C}P^{2n+1}$ without fixed point?
complex-analysis fixed-point-theorems projective-space
complex-analysis fixed-point-theorems projective-space
asked Nov 20 '18 at 16:03
Ali Taghavi
186329
asked Nov 20 '18 at 16:03
Ali Taghavi
186329
edited Nov 20 '18 at 17:38
asked Nov 20 '18 at 16:03
Ali Taghavi
186329
asked Nov 20 '18 at 16:03
Ali Taghavi
186329
asked Nov 20 '18 at 16:03
Ali Taghavi
186329
186329
add a comment |
add a comment |
1 Answer
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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.
answered Nov 20 '18 at 17:38
Ben
2,563616
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1 Answer
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1 Answer
1
active
oldest
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active
oldest
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active
oldest
votes
No. The holomorphic diffeomorphisms of $mathbb C P^n$ are $PGL_{n+1}$. These always have fixed points because every matrix has an eigenvector.
answered Nov 20 '18 at 17:38
Ben
2,563616
add a comment |
No. The holomorphic diffeomorphisms of $mathbb C P^n$ are $PGL_{n+1}$. These always have fixed points because every matrix has an eigenvector.
answered Nov 20 '18 at 17:38
Ben
2,563616
add a comment |
No. The holomorphic diffeomorphisms of $mathbb C P^n$ are $PGL_{n+1}$. These always have fixed points because every matrix has an eigenvector.
answered Nov 20 '18 at 17:38
Ben
2,563616
No. The holomorphic diffeomorphisms of $mathbb C P^n$ are $PGL_{n+1}$. These always have fixed points because every matrix has an eigenvector.
answered Nov 20 '18 at 17:38
Ben
2,563616
edited Nov 20 '18 at 17:55
answered Nov 20 '18 at 17:38
Ben
2,563616
answered Nov 20 '18 at 17:38
Ben
2,563616
answered Nov 20 '18 at 17:38
Ben
2,563616
2,563616
add a comment |
add a comment |
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