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Apolarity, Hessian and Macaulay polynomials

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journal contribution
posted on 02.06.2017, 13:04 authored by Lorenzo Di Biagio, Elisa Postinghel
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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Communications in Algebra

Volume

41

Issue

1

Pages

226 - 237

Citation

DI BIAGIO, L. and POSTINGHEL, E., 2013. Apolarity, Hessian and Macaulay Polynomials. Communications in Algebra, 41(1), pp. 226-237.

Publisher

© Taylor & Francis

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2013

Notes

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

ISSN

0092-7872

eISSN

1532-4125

Language

en