Geometry of syzygies via Poncelet varieties
| dc.creator | Ilardi, Giovanna | |
| dc.creator | Supino, Paola | |
| dc.creator | Vallès, Jean | |
| dc.date | 2008-06-30 | |
| dc.date.accessioned | 2026-07-07T12:19:44Z | |
| dc.date.available | 2026-07-07T12:19:44Z | |
| dc.description | We consider the Grassmannian $\mathbb{G}r(k,n)$ of $(k+1)$-dimensional linear subspaces of $V_n=H^0({¶^1},Ø_{¶^1}(n))$. We define $\frak{X}_{k,r,d}$ as the classifying space of the $k$-dimensional linear systems of degree $n$ on $¶^1$ whose basis realize a fixed number of polynomial relations of fixed degree, say a fixed number of syzygies of a certain degree. The first result of this paper is the computation of the dimension of $\frak{X}_{k,r,d}$. In the second part we make a link between $\frak{X}_{k,r,d}$ and the Poncelet varieties. In particular, we prove that the existence of linear syzygies implies the existence of singularities on the Poncelet varieties. | |
| dc.identifier | https://arxiv.org/abs/0806.4881 | |
| dc.identifier | http://arxiv.org/abs/0806.4881 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212857 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J60, 14J10, 14J25 | |
| dc.title | Geometry of syzygies via Poncelet varieties | |
| dc.type | text |