Weakly Proper Toric Quotients

Details Weakly Proper Toric Quotients Weakly Proper Toric Quotients

2000-03-29

arxiv.org/abs/math/0003204v3

Mathematics

Algebraic Geometry

23 pages, 9 figures, amslateX + pstex; this revised version has a new title and an improved introduction; several typos are co

Scientific paper

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 in fact 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.

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