Apolarity, Hessian and Macaulay polynomials

Details Apolarity, Hessian and Macaulay polynomials Apolarity, Hessian and Macaulay polynomials

2010-07-28

arxiv.org/abs/1007.4891v1

Mathematics

Algebraic Geometry

10 pages

Scientific paper

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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