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Dec 5, 2017 at 1:40 comment added user21574 For the first part of your question : It is due to holomorphic slice theorem, see p.18 and Theorem 2.6 of arxiv.org/pdf/alg-geom/9304004.pdf . This gives a right answer to the first part of your question. It seems that Sjamaar first solved this question in 1993 . About part 2 .in your case , symplectic quotiens are birational together due to V. Guillemin and S. Sternberg, Birational equivalence in the symplectic category, Invent. Math. 97 (1989), 485–522
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Jun 15, 2017 at 14:40 history edited Michael Albanese CC BY-SA 3.0
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