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Nov 24 at 20:54 comment added Mathmop thanks both for the references!
Nov 23 at 19:33 comment added Jason Starr It is also discussed in Dolgachev’s book on invariant theory.
Nov 20 at 17:03 comment added abx No, even if $G$ acts freely. You need more, namely a $G$-linearization on your line bundle. I suggest the first chapter of Mumford's GIT, where this is clearly explained.
Nov 20 at 11:07 history asked Mathmop CC BY-SA 4.0