Weakly proper toric quotients

Annette A'Campo-Neuen ¹

¹ Mathematisches Institut Universität Basel Rheinsprung 21 CH-4051 Basel, Switzerland

Colloquium Mathematicum, Tome 102 (2005) no. 2, pp. 155-180

Résumé

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.

Détail

DOI : 10.4064/cm102-2-1

Keywords: consider subtorus actions complex toric varieties natural candidate categorical quotient action so called toric quotient universal object constructed toric category prove toric quotient weakly proper addition quotient variety expected dimension toric quotient categorical quotient category algebraic varieties example weak properness always holds toric quotient subtorus action toric variety whose fan has convex support