arXiv subjects
Publications and source records attributed to Mihaela Popoviciu.
We consider the degrees of the elements of a homogeneous system of parameters for the ring of invariants of a binary form, give a divisibility condition, and a complete classification for forms of degree at most 8.
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.
Let Vn be the SL2-module of binary forms of degree n and let V = Vn1+...+Vnp . We consider the algebra R of polynomial functions on V invariant under the action of SL2. The measure of the intricacy of these algebras is the length of their chains of syzygies, called homological dimension hdR. Popov gave in 1983 a classification of the cases in which hdR <=10 for a single binary form (p = 1) or hdR <=3 for a system of two or more binary forms (p > 1). We extend Popov's result and determine for p = 1 the cases with hdR <= 100, and for p > 1 those with hdR <= 15. In these cases we give a set of homogeneous parameters and a set of generators for the algebra R.
We consider the algebra of invariants of binary forms of degree 10 with complex coefficients, construct a system of parameters with degrees 2, 4, 6, 6, 8, 9, 10, 14 and find the 106 basic invariants.
We consider the algebra of invariants of binary forms of degree 9 with complex coefficients, find the 92 basic invariants, give an explicit system of parameters and show the existence of four more systems of parameters with different sets of degrees.