On quadratic and higher normality of small codimension projective varieties
| dc.creator | Brandigi, Chiara | |
| dc.date | 2000-02-17 | |
| dc.date | 2000-02-29 | |
| dc.date.accessioned | 2026-07-07T04:33:55Z | |
| dc.date.available | 2026-07-07T04:33:55Z | |
| dc.description | Ran proved that smooth codimension 2 varieties in ${\bf P}^{m+2}$ are $j$-normal if $(j+1)(3j-1)\le m-1$, in this paper we extend this result to small codimension projective varieties. Let $X$ be a r codimension subvariety of $\pro$, we prove that if the set $Σ_{(j+1)}$ of $(j+1)$-secants to $X$ through a generic external point is not empty, $2(r+1)j\leq m-r$ and $(j+1)((r+1)j-1)\leq m-1$ then $X$ is $j$-normal. If $X$ is given by the zero locus of a section of a rank $r$ vector bundle $E$ on $\pro$, we prove that $\textrm{deg} Σ_{j+1}=\frac{1}{(j+1)!}\prod_{i=0}^{j}c_{r}(E(-i))$. Moreover we get a new simple proof of Zak's theorem on linear normality if $m\ge 3r$. Finally we prove that if $c_{r}(N(-2))\neq 0$ and $6r\le m-4$ then $X$ is 2-normal. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0002140 | |
| dc.identifier | http://arxiv.org/abs/math/0002140 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58711 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14M07,14N05,14N10 | |
| dc.title | On quadratic and higher normality of small codimension projective varieties | |
| dc.type | text |