Sylvester versus Gundelfinger (Q352375)

Let \(V_n\) be the \(\mathrm{SL}_2\) module of binary forms of degree \(n\) and \(V = V_1 \oplus V_3 \oplus V_4\). This paper shows that the invariant ring \(\mathbb{C}[V]^{\mathrm{SL}_2}\) has 63 minimal generators of degree at most~11. These days this is not a too complicated endeavour since we know that the invariant ring is Cohen-Macaulay and thus has a homogeneous system of parameters. The authors identify such a system to get their result.NEWLINENEWLINEThe paper also contains a very nice historical account, culminating in a correction of a table of \textit{Groundforms} published by Sylvester in the second volume of Amer. Jour. Math in 1879.