Symmetric rank of some reducible quartics
Abstract
Abstract In this paper we study the symmetric rank of products of linear forms and an irreducible quadratic form. The main result presents a new, non-trivial lower bound for the rank, and the arguments rely on the apolarity lemma. In the special case of degree 4 we give a list of normal forms for such quartics, and we apply our general result to compute the rank of almost all of them. These families of quartics provide examples of polynomials of generic, supergeneric, and even maximal rank.
Fields of Study & Subjects
Advanced Algebra and Geometry
Finite Group Theory Research
Tensor decomposition and applications
Publication details
- Journal / source
- Annali di Matematica Pura ed Applicata (1923 -)
- Publisher
- Springer Science and Business Media LLC
- Volume
- 205
- Issue
- 3
- Pages
- 1615–1636
- Publication date
- 2 January 2026
- Language
- EN