Quotients of an affine variety by an action of a torus
Let X be an affine T-variety. We study two different quotients for the action of T on X: the toric Chow quotient X/C T and the toric Hilbert scheme H. We introduce a notion of the main component H 0 of H, which parameterizes general T-orbit closures in X and their flat limits. The main component U 0 of the universal family U over H is a preimage of H 0. We define an analogue of a universal family WX over the main component of X/C T. We show that the toric Chow morphism restricted on the main components...