Factorially graded rings of complexity one

Details Factorially graded rings of complexity one Factorially graded rings of complexity one

2010-05-23

arxiv.org/abs/1005.4194v3

Mathematics

Algebraic Geometry

minor revision, 10 pages

Scientific paper

We consider finitely generated normal algebras over an algebraically closed field of characteristic zero that come with a complexity one grading by a finitely generated abelian group such that the conditions of a UFD are satisfied for homogeneous elements. Our main results describe these algebras in terms of generators and relations. We apply this to write down explicitly the possible Cox rings of normal complete rational varieties with a complexity one torus action.

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