Reductive group actions on affine varieties and their doubling

Dmitri I. Panyushev

Annales de l'institut Fourier (1995)

  • Volume: 45, Issue: 4, page 929-950
  • ISSN: 0373-0956

Abstract

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We study G -actions of the form ( G : X × X * ) , where X * is the dual (to X ) G -variety. These actions are called the doubled ones. A geometric interpretation of the complexity of the action ( G : X ) is given. It is shown that the doubled actions have a number of nice properties, if X is spherical or of complexity one.

How to cite

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Panyushev, Dmitri I.. "Reductive group actions on affine varieties and their doubling." Annales de l'institut Fourier 45.4 (1995): 929-950. <http://eudml.org/doc/75151>.

@article{Panyushev1995,
abstract = {We study $G$-actions of the form $(G:X\times X^\{*\})$, where $X^\{*\}$ is the dual (to $X$) $G$-variety. These actions are called the doubled ones. A geometric interpretation of the complexity of the action $(G:X)$ is given. It is shown that the doubled actions have a number of nice properties, if $X$ is spherical or of complexity one.},
author = {Panyushev, Dmitri I.},
journal = {Annales de l'institut Fourier},
keywords = {algebra of invariants; doubled actions; complexity of the action; spherical variety},
language = {eng},
number = {4},
pages = {929-950},
publisher = {Association des Annales de l'Institut Fourier},
title = {Reductive group actions on affine varieties and their doubling},
url = {http://eudml.org/doc/75151},
volume = {45},
year = {1995},
}

TY - JOUR
AU - Panyushev, Dmitri I.
TI - Reductive group actions on affine varieties and their doubling
JO - Annales de l'institut Fourier
PY - 1995
PB - Association des Annales de l'Institut Fourier
VL - 45
IS - 4
SP - 929
EP - 950
AB - We study $G$-actions of the form $(G:X\times X^{*})$, where $X^{*}$ is the dual (to $X$) $G$-variety. These actions are called the doubled ones. A geometric interpretation of the complexity of the action $(G:X)$ is given. It is shown that the doubled actions have a number of nice properties, if $X$ is spherical or of complexity one.
LA - eng
KW - algebra of invariants; doubled actions; complexity of the action; spherical variety
UR - http://eudml.org/doc/75151
ER -

References

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