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2009 An invariant regarding Waring's problem for cubic polynomials
Giorgio Ottaviani
Nagoya Math. J. 193: 95-110 (2009).

Abstract

We compute the equation of the 7-secant variety to the Veronese variety $({\bf P}^{4}, \mathcal{O}(3))$, 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.

Citation

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Giorgio Ottaviani. "An invariant regarding Waring's problem for cubic polynomials." Nagoya Math. J. 193 95 - 110, 2009.

Information

Published: 2009
First available in Project Euclid: 3 March 2009

zbMATH: 1205.14064
MathSciNet: MR2502909

Subjects:
Primary: 14L35 , 14M12 , 14M20 , 15A72

Rights: Copyright © 2009 Editorial Board, Nagoya Mathematical Journal

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Vol.193 • 2009
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