# Quotients of an affine variety by an action of a torus

Olga Chuvashova; Nikolay Pechenkin

Open Mathematics (2013)

- Volume: 11, Issue: 11, page 1863-1880
- ISSN: 2391-5455

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topOlga Chuvashova, and Nikolay Pechenkin. "Quotients of an affine variety by an action of a torus." Open Mathematics 11.11 (2013): 1863-1880. <http://eudml.org/doc/269742>.

@article{OlgaChuvashova2013,

abstract = {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.},

author = {Olga Chuvashova, Nikolay Pechenkin},

journal = {Open Mathematics},

keywords = {Torus action; Toric variety; Toric Chow quotient; Toric Hilbert scheme; torus action; toric variety; toric Chow quotient; toric Hilbert scheme},

language = {eng},

number = {11},

pages = {1863-1880},

title = {Quotients of an affine variety by an action of a torus},

url = {http://eudml.org/doc/269742},

volume = {11},

year = {2013},

}

TY - JOUR

AU - Olga Chuvashova

AU - Nikolay Pechenkin

TI - Quotients of an affine variety by an action of a torus

JO - Open Mathematics

PY - 2013

VL - 11

IS - 11

SP - 1863

EP - 1880

AB - 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.

LA - eng

KW - Torus action; Toric variety; Toric Chow quotient; Toric Hilbert scheme; torus action; toric variety; toric Chow quotient; toric Hilbert scheme

UR - http://eudml.org/doc/269742

ER -

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