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May 6, 2019 at 17:01 comment added Sean Lawton A point is a variety. A GIT quotient is not "the" quotient. There are more than one. For affine varieties, the point is the quotient. But in the quasi-projective setting there are more than one. Each depends on a line bundle, in this case, a character. The trivial character gives the affine quotient, whereas the identity character gives your construction. See math.stackexchange.com/a/2022872/84231 for a more general description and reference.
May 6, 2019 at 15:13 history edited user130124 CC BY-SA 4.0
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May 6, 2019 at 4:13 history edited user130124 CC BY-SA 4.0
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May 6, 2019 at 3:53 history answered user130124 CC BY-SA 4.0