What do we lose if we only consider quasi-projective varieties? What are merits of considering varieties which are not quasi-projective?
What do we lose if we only consider quasi-projective varieties?
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algebraic-geometry
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4Seems a reasonable question to me, so I upvoted. – 2012-12-30
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0This is a good question. But it could be a little more precise: what do you mean by varieties ? Are they separated or do you even restrict to proper varieties ? – 2012-12-30
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0@QiL They are varieties in the sense of Serre, i.e. they are separated and not necessarily proper. – 2012-12-30
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1Separated algebraic varieties are open subvarieties of proper algebraic varieties by a theorem of Nagata. So I think the real question would be why to consider proper varieties which are not necessarily projective. – 2012-12-30
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0@QiL "So I think the real question would be why to consider proper varieties which are not necessarily projective." I would like to know the reason why. – 2012-12-30
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0I'm curious to know who voted to close. – 2012-12-31
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1@MakotoKato: Not to nitpick, but what *is* interesting, is not *who* voted to close, but the *reason* why. Anyhow, I think this is a good question. – 2012-12-31
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0**I have removed off-topic comments.** – 2013-01-02
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0I noticed that someone serially upvoted for my questions and answers including this one. While I appreciate them, I would like to point out that serial upvotes are automatically reversed by the system. – 2013-11-27