Consider an algebraic torus of small dimension acting on an open subset of a
complex vector space, or more generally on a quasiaffine variety such that a
separated orbit space exists. We discuss under which conditions this orbit
space is quasiprojective. One of our counterexamples provides a toric variety
with enough effective invariant Cartier divisors that is not embeddable into a
smooth toric variety.Comment: 11 pages, 1 figur