Weakly proper toric quotients

Annette A'Campo-Neuen. "Weakly proper toric quotients." Colloquium Mathematicae 102.2 (2005): 155-180. <http://eudml.org/doc/283897>.

@article{AnnetteACampo2005,
abstract = {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.},
author = {Annette A'Campo-Neuen},
journal = {Colloquium Mathematicae},
keywords = {toric variety; toric prevariety; system of fans; categorical quotient; subtorus action},
language = {eng},
number = {2},
pages = {155-180},
title = {Weakly proper toric quotients},
url = {http://eudml.org/doc/283897},
volume = {102},
year = {2005},
}

TY - JOUR
AU - Annette A'Campo-Neuen
TI - Weakly proper toric quotients
JO - Colloquium Mathematicae
PY - 2005
VL - 102
IS - 2
SP - 155
EP - 180
AB - 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.
LA - eng
KW - toric variety; toric prevariety; system of fans; categorical quotient; subtorus action
UR - http://eudml.org/doc/283897
ER -