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Title: Apolarity, Hessian and Macaulay polynomials
Authors: Di Biagio, Lorenzo
Postinghel, Elisa
Keywords: Apolarity
Hessian polynomial
Jacobian ring
Macaulay correspondence
Issue Date: 2013
Publisher: © Taylor & Francis
Citation: DI BIAGIO, L. and POSTINGHEL, E., 2013. Apolarity, Hessian and Macaulay Polynomials. Communications in Algebra, 41(1), pp. 226-237.
Abstract: A result by Macaulay states that an Artinian graded Gorenstein ring R of socle dimension one and socle degree δ can be realized as the apolar ring ℂ[∂/∂x0,...,∂/∂xn]/g⊥of a homogeneous polynomial g of degree δ in x0,..., xn. If R is the Jacobian ring of a smooth hypersurface f(x0,..., xn) = 0, then δ is equal to the degree of the Hessian polynomial of f. In this article we investigate the relationship between g and the Hessian polynomial of f, and we provide a complete description for n = 1 and deg(f) ≤4 and for n = 2 and deg(f) ≤3. © 2013 Copyright Taylor and Francis Group, LLC.
Description: This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Algebra on 04 Jan 2013, available online: http://dx.doi.org/10.1080/00927872.2011.629265
Version: Accepted for publication
DOI: 10.1080/00927872.2011.629265
URI: https://dspace.lboro.ac.uk/2134/25239
Publisher Link: http://dx.doi.org/10.1080/00927872.2011.629265
ISSN: 0092-7872
Appears in Collections:Published Articles (Maths)

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