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Jun 25, 2019 at 10:44 comment added Nick L The blow of a smooth variety in a point is always a smooth variety (in particular it is a complex manifold). The examples I gave are smooth toric surfaces.
Jun 25, 2019 at 8:45 comment added BrianT I'm not a specialist of toric surfaces and blow ups, but is it possible that your answer holds only for non smooth toric varieties ? My question was for toric manifolds.
Jun 24, 2019 at 8:02 comment added BrianT Thanks a lot for your answer.
Jun 24, 2019 at 2:50 history edited Nick L CC BY-SA 4.0
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Jun 23, 2019 at 23:36 history answered Nick L CC BY-SA 4.0