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2 days ago comment added User43029 So, I took a look at Mumford's book, but this is not quite yet what I am asking. I understand things could go wrong in the quotient and that is why he developed the theory of quotients with linearized sheaves, but what I am looking for is a concrete example where the quotient does not work, besides the classical one of C^* acting on A^n, because there, the action is not free.
Dec 10 at 6:06 comment added abx Yes. Have a look at Mumford's Geometric Invariant Theory, chapter I.
Dec 9 at 21:13 comment added User43029 Ok, I am assuming that the quotient space is indeed a scheme. Is it too strong?
Dec 9 at 10:22 comment added abx Irreducible components of what?
S Dec 9 at 9:42 history bounty started User43029
S Dec 9 at 9:42 history notice added User43029 Draw attention
Dec 5 at 14:23 history edited LSpice CC BY-SA 4.0
Capitalise title; name of link; TeX
Dec 5 at 9:16 history asked User43029 CC BY-SA 4.0