Cox rings of rational complexity one T-varieties

Details Cox rings of rational complexity one T-varieties Cox rings of rational complexity one T-varieties

2010-09-02

arxiv.org/abs/1009.0478v1

Mathematics

Algebraic Geometry

17 pages, 5 figures

Scientific paper

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 covering of the projective line P^1 which corresponds to the affine spectrum of the Cox ring of X. This description allows for a detailed study of torus orbits and deformations of the latter. Moreover, we present coverings of P^1 together with an action of a finite abelian group A in terms of so-called A-divisors of degree zero on P^1.

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