Log terminal singularities, platonic tuples and iteration of Cox rings

Abstract

Looking at the well understood case of log terminal surface singularities, one observes that each of them is the quotient of a factorial one by a finite solvable group. The derived series of this group reflects an iteration of Cox rings of surface singularities. We extend this picture to log terminal singularities in any dimension coming with a torus action of complexity one. In this setting, the previously finite groups become solvable torus extensions. As explicit examples, we investigate compound du Val threefold singularities. We give a complete classification and exhibit all the possible chains of iterated Cox rings.

Minor revision, 56 pages

References in corpus (2)

• Non-complete rational T-varieties of complexity one
• On terminal Fano 3-folds with 2-torus action

Cited by in corpus (15)

• On iteration of Cox rings
• Rational Complexity-One T-Varieties are Well-Poised
• Iteration of Cox rings of klt singularities
• On the anticanonical complex
• Polynomial curves on trinomial hypersurfaces
• Reductive quotients of klt singularities
• Cox rings of almost homogeneous SL2-threefolds
• The anticanonical complex for non-degenerate toric complete intersections
• On Gorenstein Fano Threefolds with an Action of a Two-Dimensional Torus
• Classifying log del Pezzo surfaces with torus action
• Completing the classification of representations of ${\mathrm{SL}}_n$ with complete intersection invariant ring
• Del Pezzo surfaces of Picard number one admitting a torus action
• Affine cones as images of affine spaces
• On terminal Fano 3-folds with 2-torus action, part II
• The cone of curves and the Cox ring of rational surfaces over Hirzebruch surfaces