European Journal of Mathematics

, Volume 4, Issue 1, pp 242–312 | Cite as

Log terminal singularities, platonic tuples and iteration of Cox rings

  • Ivan Arzhantsev
  • Lukas Braun
  • Jürgen HausenEmail author
  • Milena Wrobel
Research Article


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.


Log terminal singularities Cox rings Torus action of complexity one 

Mathematics Subject Classification

14L30 14M25 14B05 13A05 13F15 



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


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Ivan Arzhantsev
    • 1
  • Lukas Braun
    • 2
  • Jürgen Hausen
    • 2
    Email author
  • Milena Wrobel
    • 2
  1. 1.Faculty of Computer ScienceNational Research University Higher School of EconomicsMoscowRussia
  2. 2.Mathematisches InstitutUniversität TübingenTübingenGermany

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