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arXiv · 1007.4891

Apolarity, Hessian and Macaulay polynomials

Lorenzo Di Biagio·Elisa Postinghel
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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.

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Lorenzo Di Biagio, Elisa Postinghel. 2012-10-08. Apolarity, Hessian and Macaulay polynomials. https://doi.org/10.1080/00927872.2011.629265

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