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Trudy Mat. Inst. Steklova, 2009, Volume 264, Pages 152–164 (Mi tm803)  

This article is cited in 8 scientific papers (total in 8 papers)

Two Orbits: When Is One in the Closure of the Other?

V. L. Popov

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

Abstract: Let $G$ be a connected linear algebraic group, let $V$ be a finite dimensional algebraic $G$-module, and let $\mathcal O_1$ and $\mathcal O_2$ be two $G$-orbits in $V$. We describe a constructive way to find out whether or not $\mathcal O_1$ lies in the closure of $\mathcal O_2$.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2009, 264, 146–158

Bibliographic databases:

UDC: 512.7
Received in August 2008

Citation: V. L. Popov, “Two Orbits: When Is One in the Closure of the Other?”, Multidimensional algebraic geometry, Collected papers. Dedicated to the Memory of Vasilii Alekseevich Iskovskikh, Corresponding Member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 264, MAIK Nauka/Interperiodica, Moscow, 2009, 152–164; Proc. Steklov Inst. Math., 264 (2009), 146–158

Citation in format AMSBIB
\by V.~L.~Popov
\paper Two Orbits: When Is One in the Closure of the Other?
\inbook Multidimensional algebraic geometry
\bookinfo Collected papers. Dedicated to the Memory of Vasilii Alekseevich Iskovskikh, Corresponding Member of the Russian Academy of Sciences
\serial Trudy Mat. Inst. Steklova
\yr 2009
\vol 264
\pages 152--164
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\jour Proc. Steklov Inst. Math.
\yr 2009
\vol 264
\pages 146--158

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    This publication is cited in the following articles:
    1. Bürgisser P., Landsberg J.M., Manivel L., Weyman J., “An overview of mathematical issues arising in the geometric complexity theory approach to VP$\ne$VNP”, SIAM J. Comput., 40:4 (2011), 1179–1209  crossref  mathscinet  zmath  isi  scopus
    2. S. N. Fedotov, “Framed moduli spaces and tuples of operators”, J. Math. Sci., 193:4 (2013), 606–621  mathnet  crossref
    3. de Graaf W.A., Vinberg E.B., Yakimova O.S., “An Effective Method to Compute Closure Ordering for Nilpotent Orbits of Theta-Representations”, J. Algebra, 371 (2012), 38–62  crossref  mathscinet  zmath  isi  scopus
    4. Osinovskaya A.A., Suprunenko I.D., “Stabilizers and Orbits of First Level Vectors in Modules for the Special Linear Groups”, J. Group Theory, 16:5 (2013), 719–743  crossref  mathscinet  zmath  isi  elib  scopus
    5. Benes T., Burde D., “Classification of Orbit Closures in the Variety of Three-Dimensional Novikov Algebras”, J. Algebra. Appl., 13:2 (2014), 1350081  crossref  mathscinet  zmath  isi  scopus
    6. de Graaf W.A., “Orbit Closures of Linear Algebraic Groups”, Computer Algebra and Polynomials, Lecture Notes in Computer Science, 8942, eds. Gutierrez J., Schicho J., Weimann M., Springer-Verlag Berlin, 2015, 76–93  crossref  mathscinet  zmath  isi  scopus
    7. Derksen H., Kemper G., “Is One of the Two Orbits in the Closure of the Other?”: Derksen, H Kemper, G, Computational Invariant Theory, 2Nd Edition, Encyclopaedia of Mathematical Sciences, 130, Springer-Verlag Berlin, 2015, 309–322  mathscinet  isi
    8. Ivanova N.M., Pallikaros Ch.A., “On Degenerations of Algebras Over An Arbitrary Field”, Adv. Group Theory Appl., 7 (2019), 39–83  crossref  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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