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.

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Acknowledgements

We would like thank the referee for carefully reading the manuscript and for many helpful remarks.

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Correspondence to Jürgen Hausen.

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Arzhantsev, I., Braun, L., Hausen, J. et al. Log terminal singularities, platonic tuples and iteration of Cox rings. European Journal of Mathematics 4, 242–312 (2018). https://doi.org/10.1007/s40879-017-0179-8

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Keywords

  • Log terminal singularities
  • Cox rings
  • Torus action of complexity one

Mathematics Subject Classification

  • 14L30
  • 14M25
  • 14B05
  • 13A05
  • 13F15