Apolarity, Hessian and Macaulay polynomials
Algebraic Geometry
2012-10-09 v2 Commutative Algebra
Abstract
A result by Macaulay states that an Artinian graded Gorenstein ring R of socle dimension one and socle degree b can be realized as the apolar ring of a homogeneous polynomial f of degree b. If R is the Jacobian ring of a smooth hypersurface g=0, then b is just equal to the degree of the Hessian polynomial of g. In this paper we investigate the relationship between f and the Hessian polynomial of g.
Cite
@article{arxiv.1007.4891,
title = {Apolarity, Hessian and Macaulay polynomials},
author = {Lorenzo Di Biagio and Elisa Postinghel},
journal= {arXiv preprint arXiv:1007.4891},
year = {2012}
}
Comments
12 pages. Improved exposition, minor corrections