Mathematische Annalen

, Volume 334, Issue 3, pp 557–607 | Cite as

Polyhedral divisors and algebraic torus actions

  • Klaus AltmannEmail author
  • Jürgen Hausen


We provide a complete description of normal affine varieties with effective algebraic torus action in terms of what we call proper polyhedral divisors on semiprojective varieties. Our approach extends classical cone constructions of Dolgachev, Demazure and Pinkham to the multigraded case, and it comprises the theory of affine toric varieties.

Mathematics Subject Classification (2000)

14L24 14L30 14M25 13A50 


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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Fachbereich Mathematik und InformatikFreie Universität BerlinBerlinGermany
  2. 2.Mathematisches InstitutUniversität TübingenTübingenGermany

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