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SIGMA, 2012, Volume 8, 075, 7 pages (Mi sigma752)  

This article is cited in 2 scientific papers (total in 2 papers)

Sylvester versus Gundelfinger

Andries E. Brouwera, Mihaela Popoviciub

a Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
b Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051 Basel, Switzerland

Abstract: Let $V_n$ be the $\mathrm{SL}_2$-module of binary forms of degree $n$ and let $V=V_1\oplus V_3\oplus V_4$. We show that the minimum number of generators of the algebra $R = \mathbb C[V]^{\mathrm{SL}_2}$ of polynomial functions on $V$ invariant under the action of $\mathrm{SL}_2$ equals 63. This settles a 143-year old question.

Keywords: invariants; covariants; binary forms.

DOI: https://doi.org/10.3842/SIGMA.2012.075

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Full text: http://emis.mi.ras.ru/.../075
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Bibliographic databases:

MSC: 13A15; 68W30
Received: July 18, 2012; in final form October 12, 2012; Published online October 19, 2012
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Citation: Andries E. Brouwer, Mihaela Popoviciu, “Sylvester versus Gundelfinger”, SIGMA, 8 (2012), 075, 7 pp.

Citation in format AMSBIB
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\by Andries E. Brouwer, Mihaela Popoviciu
\paper Sylvester versus Gundelfinger
\jour SIGMA
\yr 2012
\vol 8
\papernumber 075
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. Olive, “About Gordan's algorithm for binary forms”, Found. Comput. Math., 17:6 (2017), 1407–1466  crossref  mathscinet  zmath  isi  scopus
    2. R. Lercier, M. Olive, “Covariant algebra of the binary nonic and the binary decimic”, Arithmetic, Geometry, Cryptography and Coding Theory, Contemporary Mathematics, 686, eds. A. Bassa, A. Couvreur, D. Kohel, Amer. Math. Soc., 2017, 65–91  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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