Apolarity.pdf (320.51 kB)
Download fileApolarity, Hessian and Macaulay polynomials
journal contribution
posted on 2017-06-02, 13:04 authored by Lorenzo Di Biagio, Elisa PostinghelA 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 AlgebraVolume
41Issue
1Pages
226 - 237Citation
DI BIAGIO, L. and POSTINGHEL, E., 2013. Apolarity, Hessian and Macaulay Polynomials. Communications in Algebra, 41(1), pp. 226-237.Publisher
© Taylor & FrancisVersion
- 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
2013Notes
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/10.1080/00927872.2011.629265ISSN
0092-7872eISSN
1532-4125Publisher version
Language
- en