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An Invariant Regarding Waring’s Problem for Cubic Polynomials

Published online by Cambridge University Press:  11 January 2016

Giorgio Ottaviani
Giorgio Ottaviani*
Affiliation:
Dipartimento di Matematica U. Dini, Università di Firenze, viale Morgagni 67/A, 50134 Firenze, Italy, ottavian@math.unifi.it
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Abstract

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We compute the equation of the 7-secant variety to the Veronese variety (P4,O(3)), its degree is 15. This is the last missing invariant in the Alexander-Hirschowitz classification. It gives the condition to express a homogeneous cubic polynomial in 5 variables as the sum of 7 cubes (Waring problem). The interesting side in the construction is that it comes from the determinant of a matrix of order 45 with linear entries, which is a cube. The same technique allows to express the classical Aronhold invariant of plane cubics as a pfaffian.

Keywords

15A7214L3514M1214M20

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 193 , 2009, pp. 95 - 110
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2009

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