Weakly proper toric quotients

Tom 102 / 2005

Annette A'Campo-Neuen Colloquium Mathematicum 102 (2005), 155-180 MSC: 14M25, 14L30, 14D25. DOI: 10.4064/cm102-2-1


We consider subtorus actions on complex toric varieties. A natural candidate for a categorical quotient of such an action is the so-called toric quotient, a universal object constructed in the toric category. We prove that if the toric quotient is weakly proper and if in addition the quotient variety is of expected dimension then the toric quotient is a categorical quotient in the category of algebraic varieties. For example, weak properness always holds for the toric quotient of a subtorus action on a toric variety whose fan has a convex support.


  • Annette A'Campo-NeuenMathematisches Institut
    Universität Basel
    Rheinsprung 21
    CH-4051 Basel, Switzerland

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