An invariant regarding Waring's problem for cubic polynomials
| dc.creator | Ottaviani, Giorgio | |
| dc.date | 2007-12-15 | |
| dc.date.accessioned | 2026-07-07T08:49:32Z | |
| dc.date.available | 2026-07-07T08:49:32Z | |
| dc.description | 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. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/0712.2527 | |
| dc.identifier | http://arxiv.org/abs/0712.2527 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144331 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 15A72; 14L35; 14M12; 14M20 | |
| dc.title | An invariant regarding Waring's problem for cubic polynomials | |
| dc.type | text |