Codimension one decompositions and Chow varieties
| dc.creator | Carlini, E. | |
| dc.date | 2004-10-28 | |
| dc.date.accessioned | 2026-07-07T05:13:46Z | |
| dc.date.available | 2026-07-07T05:13:46Z | |
| dc.description | A presentation of a degree $d$ form in $n+1$ variables as the sum of homogenous elements ``essentially'' involving $n$ variables is called a {\em codimension one decomposition}. Codimension one decompositions are introduced and the related Waring Problem is stated and solved. Natural schemes describing the codimension one decompositions of a generic form are defined. Dimension and degree formulae for these schemes are derived when the number of summands is the minimal one; in the zero dimensional case the scheme is showed to be reduced. These results are obtained by studying the Chow variety $Δ_{n,s}$ of zero dimensional degree $s$ cycles in $\PP^n$. In particular, an explicit formula for $\degΔ_{n,s}$ is determined. | |
| dc.identifier | https://arxiv.org/abs/math/0410602 | |
| dc.identifier | http://arxiv.org/abs/math/0410602 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73036 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.title | Codimension one decompositions and Chow varieties | |
| dc.type | text |