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Nov 17, 2020 at 21:50 comment added Francesco Polizzi Ok, I see. I was confused by "any such sequence" at the beginning of the second part of the answer.
Nov 17, 2020 at 21:00 comment added user127776 The explanation given above for proper variety is general. It is not specialized to the specific short exact sequence of trivial bundles given at the start.
Nov 17, 2020 at 20:37 comment added Francesco Polizzi Does this really refute my example? My middle term is not balanced, how do you reduce yourself to the case of the sum of two trivial bundles?
Nov 17, 2020 at 20:11 comment added Nicolas Hemelsoet @user127776 : I think the explanation is given by my comment below
Nov 17, 2020 at 20:11 vote accept user127776
Nov 17, 2020 at 20:11 comment added user127776 Yes my $X$ is proper. Your argument is super-smart. So there are no examples of such thing on projective line. This refutes one of the comments above. Thanks.
Nov 17, 2020 at 20:09 history edited SashaP CC BY-SA 4.0
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Nov 17, 2020 at 20:00 history answered SashaP CC BY-SA 4.0