Quotients of Real Algebraic Sets via Finite Groups

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.
Citation Formats
Y. Ozan, “Quotients of Real Algebraic Sets via Finite Groups,” pp. 493–499, 1997, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/80761.