Non-complete rational T-varieties of complexity one

Abstract

We consider rational varieties with a torus action of complexity one and extend the combinatorial approach via the Cox ring developed for the complete case in earlier work to the non-complete, e.g. affine, case. This includes in particular a description of all factorially graded affine algebras of complexity one with only constant homogeneous invertible elements in terms of canonical generators and relations.

13 pages

References in corpus (1)

• On terminal Fano 3-folds with 2-torus action

Cited by in corpus (13)

• Log terminal singularities, platonic tuples and iteration of Cox rings
• On torus actions of higher complexity
• On iteration of Cox rings
• On rigidity of trinomial hypersurfaces and factorial trinomial varieties
• Polynomial curves on trinomial hypersurfaces
• On homogeneous locally nilpotent derivations of trinomial algebras
• Homogeneous locally nilpotent derivations of non-factorial trinomial algebras
• On irregular Sasaki-Einstein metrics in dimension 5
• Limit points and additive group actions
• Classifying log del Pezzo surfaces with torus action
• Homogeneous locally nilpotent derivations on trinomial varieties
• The Picard index of a surface with torus action
• Crepant resolutions of 3-dimensional quotient singularities via Cox rings