Apolar Schemes of Algebraic Forms

Chipalkatti, Jaydeep

Canadian journal of mathematics, Tome 58 (2006) no. 3, pp. 476-491

Résumé

This is a note on the classical Waring's problem for algebraic forms. Fix integers $(n,d,r,s)$ , and let $\Lambda $ be a general $r$ -dimensional subspace of degree $d$ homogeneous polynomials in $n+1$ variables. Let $\mathcal{A}$ denote the variety of $s$ -sided polar polyhedra of $\Lambda $ . We carry out a case-by-case study of the structure of $\mathcal{A}$ for several specific values of $(n,d,r,s)$ . In the first batch of examples, $\mathcal{A}$ is shown to be a rational variety. In the second batch, $\mathcal{A}$ is a finite set of which we calculate the cardinality.

Détail

DOI : 10.4153/CJM-2006-020-3

Mots-clés : 14N05, 14N15, Waring's problem, apolarity, polar polyhedron

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