An Invariant regarding Waring’s Problem for Cubic Polynomials
نویسنده
چکیده
Abstract. We compute the equation of the 7-secant variety to the Veronese variety (P,O(3)), its degree is 15. This is the last missing invariant in the AlexanderHirschowitz 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.
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تاریخ انتشار 2008