On the Wronskian combinants of binary forms - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2005

On the Wronskian combinants of binary forms

Résumé

For generic binary forms $A_1,...,A_r$ of order $d$ we construct a class of combinants $C = \{\C_q: 0 \le q \le r, q \neq 1\}$, to be called the Wronskian combinants of the $A_i$. We show that the collection $C$ gives a projective imbedding of the Grassmannian $G(r,S_d)$, and as a corollary, any other combinant admits a formula as an iterated transvectant in the $C$. Our second main result characterizes those collections of binary forms which can arise as Wronskian combinants. These collections are the ones such that an associated algebraic differential equation has the maximal number of linearly independent polynomial solutions. Along the way we deduce some identities which connect Wronskians with transvectants.

Dates et versions

hal-00086513 , version 1 (18-07-2006)

Identifiants

Citer

Abdelmalek Abdesselam, Jaydeep Chipalkatti. On the Wronskian combinants of binary forms. 2005. ⟨hal-00086513⟩
91 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More