This article is cited in 2 papers

Sylvester versus Gundelfinger

Andries E. Brouwer^a, Mihaela Popoviciu<sup>b

a</sup> 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.

MSC: 13A15; 68W30

Received: July 18, 2012; in final form October 12, 2012; Published online October 19, 2012

Language: English

DOI: 10.3842/SIGMA.2012.075

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