A proper 𝐺ₐ action on 𝐶⁵ which is not locally trivial

Abstract

Abstract. The quotient of a proper holomorphic Ga action on C" is known to carry the structure of a complex analytic manifold, and in the case of a rational algebraic action, the geometric quotient exists as an algebraic space. An example is given of a proper rational algebraic action for which the quotient is not a variety, and therefore the action is not locally trivial in the Zariski topology.