Chow points of \({\mathbb{C}}\)-orbits (Q957913)

Given an algebraic group action on a variety \(X\), one may associate to each point \(x\in X\) the (Zariski) closure of the orbit through \(x\). This defines a rational map from the variety to a Chow variety of \(X\). In the article, free algebraic actions of the additive group \(({\mathbb C},+)\) on the affine space \(({\mathbb C}^n,+)\) are studied via this map. In particular criteria are deduced which tell us when such an action is proper or has a Hausdorff quotient.