Weakly proper toric quotients

Annette A'Campo-Neuen
2005 Colloquium Mathematicum  
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
more » ... on on a toric variety whose fan has a convex support.
doi:10.4064/cm102-2-1 fatcat:52rmb55bxvhodayzgbcz2yr57m