Sylvester versus Gundelfinger

Symmetry Integrability and Geometry-Methods and Applications

article

Andries E. Brouwer¹  Mihaela Popoviciu² 

[1] Department of Mathematics and Computer Science, Technische Universiteit Eindhoven;Mathematisches Institut

关键词: invariants;    covariants;    binary forms;   

DOI  :  10.3842/SIGMA.2012.075

来源: National Academy of Science of Ukraine

【 摘 要 】

Let $V_n$ be the ${\rm SL}_2$-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 $R = \mathbb{C}[V]^{{\rm SL}_2}$ of polynomial functions on $V$ invariant under the action of ${\rm SL}_2$ equals 63. This settles a 143-year old question.

【 授权许可】

Unknown