Transformation Groups

, Volume 13, Issue 2, pp 215–242 | Cite as

Gluing Affine Torus Actions Via Divisorial Fans

  • Klaus Altmann
  • Jürgen Hausen
  • Hendrik Süss


Generalizing the passage from a fan to a toric variety, we provide a combinatorial approach to construct arbitrary effective torus actions on normal, algebraic varieties. Based on the notion of a “proper polyhedral divisor” introduced in earlier work, we develop the concept of a “divisorial fan” and show that these objects encode the equivariant gluing of affine varieties with torus action. We characterize separateness and completeness of the resulting varieties in terms of divisorial fans, and we study examples like \( \mathbb{C} \)*-surfaces and projectivizations of (nonsplit) vector bundles over toric varieties.


Vector Bundle Toric Variety Prime Divisor Cotangent Bundle Global Section 
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Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  1. 1.Fachbereich Mathematik und InformatikFreie Universität Berlin Arnimalle 3BerlinGermany
  2. 2.Mathematisches InstitutUniversität Tübingen Auf der Morgenstelle 10TübingenGermany
  3. 3.Institut für Mathematik LS Algebra und Geometrie Brandenburgische TechnischeUniversität CottbusCottbusGermany

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