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for questions on geometric invariant theory (or GIT), including stability criteria and symplectic quotients.

9 votes
3 answers
2k views

Quotient of smooth algebraic variety by proper free action of algebraic group

Let $G$ be algebraic group acting on a smooth algebraic variety $M$. Assume the action is proper and free. Is the orbit space $M/G$ an algebraic variety? If so, could someone point to a reference? If …