A generalization of the Strong Castelnuovo Lemma
| dc.creator | Ghezzi, Laura | |
| dc.date | 2008-11-22 | |
| dc.date.accessioned | 2026-07-07T10:20:28Z | |
| dc.date.available | 2026-07-07T10:20:28Z | |
| dc.description | We consider a set $X$ of distinct points in the $n$-dimensional projective space over an algebraically closed field $k$. Let $A$ denote the coordinate ring of $X$, and let $a_i(X)=\dim_k [{\rm Tor}_i^R(A,k)]_{i+1}$. Green's Strong Castelnuovo Lemma (SCL) shows that if the points are in general position, then $a_{n-1}(X)\neq 0$ if and only if the points are on a rational normal curve. Cavaliere, Rossi and Valla conjectured that if the points are not necessarily in general position the possible extension of the SCL should be the following: $a_{n-1}(X)\neq 0$ if and only if either the points are on a rational normal curve or in the union of two linear subspaces whose dimensions add up to $n$. In this work we prove the conjecture. | |
| dc.identifier | https://arxiv.org/abs/0811.3655 | |
| dc.identifier | http://arxiv.org/abs/0811.3655 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174859 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.title | A generalization of the Strong Castelnuovo Lemma | |
| dc.type | text |