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I know that there is a universal property of blow-ups in the algebraic setting (see Wikipedia).
How does this translate to the case of complex geometry and holomorphic/bimeromorphic maps? I am particularly interested in the case of a blow up of a complex orbifold.

A statement of the universal property together with a reference to the proof would be enough. But of course, I would prefer if you also write a (sketch of a) proof.
Please note that I am not very familiar with algebraic geometry, so keep things simple and smooth.

abdul
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1 Answers1

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The following proposition is from Grauert-Peternell-Remmert's Several Complex Variables, VII, page 291. The statement (2) is the universal property that you are looking for. Note that it is essentially the same as chapter II, Prop. 7.14 in Hartshorne in the algebraic setting.

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AG learner
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