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Mat. Sb. (N.S.), 1986, Volume 130(172), Number 3(7), Pages 310–334 (Mi msb1875)  

This article is cited in 30 scientific papers (total in 30 papers)

Contractions of the actions of reductive algebraic groups

V. L. Popov

Abstract: It is shown that each algebraic action of a simply connected reductive algebraic group $G$ on an affine algebraic variety $X$ can be contracted (in a flat one-dimensional family of actions) to a canonical action of $G$ on a certain affine variety $\operatorname{gr}X$ having some very special properties. It is shown that $X$ and $\operatorname{gr}X$ have many algebro-geometric properties in common. As an application, we prove the Procesi–Kraft conjecture to the effect that the singularities of the closures of orbits in the case of spherical stabilizer are rational. It is assumed that the ground field has characteristic zero.
Bibliography: 37 titles.

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English version:
Mathematics of the USSR-Sbornik, 1987, 58:2, 311–335

Bibliographic databases:

UDC: 512
MSC: Primary 14L30; Secondary 14D20, 14D25, 14M12, 14M17
Received: 10.04.1985

Citation: V. L. Popov, “Contractions of the actions of reductive algebraic groups”, Mat. Sb. (N.S.), 130(172):3(7) (1986), 310–334; Math. USSR-Sb., 58:2 (1987), 311–335

Citation in format AMSBIB
\by V.~L.~Popov
\paper Contractions of the actions of reductive algebraic groups
\jour Mat. Sb. (N.S.)
\yr 1986
\vol 130(172)
\issue 3(7)
\pages 310--334
\jour Math. USSR-Sb.
\yr 1987
\vol 58
\issue 2
\pages 311--335

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    3. Panyushev D., “Complexity and Rank of Homogeneous Spaces”, Geod. Dedic., 34:3 (1990), 249–269  mathscinet  zmath  isi
    4. D. I. Panyushev, “The canonical module of a quasihomogeneous normal affine $SL_2$-variety”, Math. USSR-Sb., 73:2 (1992), 569–578  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. I. V. Arzhantsev, “On $\operatorname{SL}_2$-actions of complexity one”, Izv. Math., 61:4 (1997), 685–698  mathnet  crossref  crossref  mathscinet  zmath  isi
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    28. A. A. Gornitskii, “Essential Signatures and Canonical Bases of Irreducible Representations of the Group $G_{2}$”, Math. Notes, 97:1 (2015), 30–41  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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