Matematicheskii Sbornik. Novaya Seriya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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.

Full text: PDF file (1681 kB)
References: PDF file   HTML file

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
\Bibitem{Pop86}
\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
\mathnet{http://mi.mathnet.ru/msb1875}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=865764}
\zmath{https://zbmath.org/?q=an:0627.14033|0613.14034}
\transl
\jour Math. USSR-Sb.
\yr 1987
\vol 58
\issue 2
\pages 311--335
\crossref{https://doi.org/10.1070/SM1987v058n02ABEH003106}


Linking options:
  • http://mi.mathnet.ru/eng/msb1875
  • http://mi.mathnet.ru/eng/msb/v172/i3/p310

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Friedrich Knop, “Weylgruppe und Momentabbildung”, Invent math, 99:1 (1990), 1  crossref  mathscinet  zmath  isi
    2. Franz Pauer, “Über gewisseG-stabile Teilmengen in projektiven Räumen”, manuscripta math, 66:1 (1990), 1  crossref  mathscinet  zmath
    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
    6. I. V. Arzhantsev, “On actions of reductive groups with one-parameter family”, Sb. Math., 188:5 (1997), 639–655  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. Dmitri I. Panyushev, “Actions of ‘nilpotent tori’ on G-varieties”, Indagationes Mathematicae, 10:4 (1999), 565  crossref  mathscinet  zmath
    8. I. V. Arzhantsev, “Contractions of affine spherical varieties”, Sb. Math., 190:7 (1999), 937–954  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. D. A. Timashev, “Equivariant compactifications of reductive groups”, Sb. Math., 194:4 (2003), 589–616  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. Alexeev V., Brion M., “Stable Reductive Varieties I: Affine Varieties”, Invent. Math., 157:2 (2004), 227–274  crossref  mathscinet  zmath  adsnasa  isi
    11. Alexeev V., Brion M., “Moduli of Affine Schemes with Reductive Group Action”, J. Algebr. Geom., 14:1 (2005), 83–117  crossref  mathscinet  zmath  isi
    12. Kaveh K., “Sagbi Bases and Degeneration of Spherical Varieties to Toric Varieties”, Mich. Math. J., 53:1 (2005), 109–121  crossref  mathscinet  zmath  isi
    13. Valery Alexeev, Michel Brion, “Stable spherical varieties and their moduli”, Internat Math Res Papers, 2006 (2006), 1  crossref  mathscinet
    14. Wilberd van der Kallen, “Finite good filtration dimension for modules over an algebra with good filtration”, Journal of Pure and Applied Algebra, 206:1-2 (2006), 59  crossref  mathscinet  zmath
    15. Michel Brion, “The total coordinate ring of a wonderful variety”, Journal of Algebra, 313:1 (2007), 61  crossref  mathscinet  zmath
    16. S. A. Gaifullin, “Affine toric $\operatorname{SL}(2)$-embeddings”, Sb. Math., 199:3 (2008), 319–339  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    17. V. Batyrev, F. Haddad, “On the Geometry of $\operatorname{SL}(2)$-Equivariant Flips”, Mosc. Math. J., 8:4 (2008), 621–646  mathnet  crossref  mathscinet  zmath
    18. Sakellaridis Y., “On the Unramified Spectrum of Spherical Varieties Over P-Adic Fields”, Compos. Math., 144:4 (2008), 978–1016  crossref  mathscinet  zmath  isi
    19. Gaitsgory D., Nadler D., “Hecke Operators on Quasimaps Into Horospherical Varieties”, Doc. Math., 14 (2009), 19–46  mathscinet  zmath  isi  elib
    20. Dennis Gaitsgory, David Nadler, “Spherical varieties and Langlands duality”, Mosc. Math. J., 10:1 (2010), 65–137  mathnet  crossref  mathscinet
    21. Rudolf Tange, “Factorisation properties of group scheme actions”, Math. Z, 2011  crossref  mathscinet
    22. Dmitri I. Panyushev, “Invariants of a maximal unipotent subgroup and equidimensionality”, Bulletin des Sciences Mathématiques, 2011  crossref  mathscinet
    23. Mitsuyasu Hashimoto, “Good filtrations and strong F-regularity of the ring of -invariants”, Journal of Algebra, 370 (2012), 198  crossref  mathscinet  zmath
    24. Arzhantsev I. Liendo A., “Polyhedral Divisors and Sl2-Actions on Affine T-Varieties”, Mich. Math. J., 61:4 (2012), 731–762  crossref  mathscinet  zmath  isi
    25. Papadakis S.A., Van Steirteghem B., “Equivariant Degenerations of Spherical Modules for Groups of Type a”, Ann. Inst. Fourier, 62:5 (2012), 1765–1809  crossref  mathscinet  zmath  isi
    26. Kiumars Kaveh, Askold G. Khovanskii, “Convex bodies associated to actions of reductive groups”, Mosc. Math. J., 12:2 (2012), 369–396  mathnet  crossref  mathscinet  zmath
    27. R. S. Avdeev, “Affine spherical homogeneous spaces with good quotient by a maximal unipotent subgroup”, Sb. Math., 203:11 (2012), 1535–1552  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    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
    29. V. S. Zhgun, “Malaya gruppa Veilya i mnogoobrazie vyrozhdennykh orisfer”, Chebyshevskii sb., 16:4 (2015), 164–187  mathnet  elib
    30. E. B. Vinberg, S. G. Gindikin, “Degeneration of Horospheres in Spherical Homogeneous Spaces”, Funct. Anal. Appl., 52:2 (2018), 83–92  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:878
    Full text:195
    References:55
    First page:2

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021