An invariant regarding Waring's problem for cubic polynomials
Ottaviani, Giorgio
arXiv, 0712.2527 / Harvested from arXiv
Text on arXiv
We compute the equation of the 7-secant variety to the Veronese variety (P^4,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 invariantof plane cubics as a pfaffian.
Publié le : 2007-12-15
Classification:  Mathematics - Algebraic Geometry,  15A72,  14L35,  14M12,  14M20 
@article{0712.2527,
     author = {Ottaviani, Giorgio},
     title = {An invariant regarding Waring's problem for cubic polynomials},
     journal = {arXiv},
     volume = {2007},
     number = {0},
     year = {2007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0712.2527}
}

Ottaviani, Giorgio. An invariant regarding Waring's problem for cubic polynomials. arXiv, Tome 2007 (2007) no. 0, . http://gdmltest.u-ga.fr/item/0712.2527/