In this paper, we will study finite algebraic group actions on real algebraic sets and compare the topological quotient X/G with the algebraic quotient X/ /G. We will give a different and shorter proof of a result of Procesi and Schwarz, stating that if the order of the group G, acting algebraically on a real algebraic set X, is odd then X/G is equal to X/ /G. In the case of even order groups, we will a give sufficient condition ( and a necessary condition in the case G = Z_2 ) for the X / G to be equal to X//G.
OZAN, Yıldıray (1997) "Quotients of Real Algebraic Sets Via Finite Groups," Turkish Journal of Mathematics: Vol. 21: No. 4, Article 12. Available at: https://journals.tubitak.gov.tr/math/vol21/iss4/12