Cox rings of rational complexity-one T-varieties

Let X be a Mori dream space together with an effective torus action of complexity one. In this note, we construct a polyhedral divisor on a suitable finite covering of P1 which corresponds to the Cox ring of X. This description allows for a detailed study of torus orbits and deformations of . Moreover, we present coverings of P1 together with an action of a finite abelian group A in terms of so-called A-divisors of degree zero on P1.