Locally trivial 𝔾a−actions on ℂ5 with singular algebraic quotients

Abstract

ABSTRACTSimple examples are given of proper algebraic actions of the additive group of complex numbers on ℂ5 whose geometric quotients are, respectively, affine, strictly quasiaffine, and algebraic spaces which are not schemes. Moreover, a Zariski locally trivial action is given whose ring of invariant regular functions defines a singular factorial affine fourfold embedded in ℂ12. The geometric quotient for the action embeds as a strictly quasiaffine variety in the smooth locus of the algebraic quotient with complement isomorphic to the normal affine surface with the A2−singularity at the origin.