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Nov 8, 2018 at 17:32 comment added Hans thanks! of course it is not a problem if they parametrize the orbits.
Nov 8, 2018 at 17:27 comment added Mattia Talpo The book of Martin Olsson is a good reference if you're willing to work through it. There's a number of other references that are shorter, for example faculty.missouri.edu/~edidind/Papers/mfile.pdf . Strictly speaking the quotient stack parametrizes orbits and not orbit closures, but I suppose this might not be a problem (depending on what you want to do with this).
Nov 8, 2018 at 8:04 comment added Hans Sounds promising. Do you have a good introductory reference for that?
Nov 7, 2018 at 23:15 comment added Mattia Talpo It seems to me that you're basically talking about the quotient stack.
Nov 7, 2018 at 20:35 history asked Hans CC BY-SA 4.0