Let X be an affine T-variety. We study two different quotients for the action of T on X: the toric Chow quotient X/C T and the toric Hilbert scheme H. We introduce a notion of the main component H 0 of H, which parameterizes general T-orbit closures in X and their flat limits. The main component U 0 of the universal family U over H is a preimage of H 0. We define an analogue of a universal family WX over the main component of X/C T. We show that the toric Chow morphism restricted on the main components lifts to a birational projective morphism from U 0 to W X. The variety W X also provides a geometric realization of the Altmann-Hausen family. In particular, the notion of W X allows us to provide an explicit description of the fan of the Altmann-Hausen family in the toric case.
@article{bwmeta1.element.doi-10_2478_s11533-013-0295-8,
author = {Olga Chuvashova and Nikolay Pechenkin},
title = {Quotients of an affine variety by an action of a torus},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {1863-1880},
zbl = {1307.14068},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0295-8}
}
Olga Chuvashova; Nikolay Pechenkin. Quotients of an affine variety by an action of a torus. Open Mathematics, Tome 11 (2013) pp. 1863-1880. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0295-8/
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