Severi varieties and their varieties of reductions
| dc.creator | Iliev, Atanas | |
| dc.creator | Manivel, Laurent | |
| dc.date | 2003-06-23 | |
| dc.date.accessioned | 2026-07-07T04:59:07Z | |
| dc.date.available | 2026-07-07T04:59:07Z | |
| dc.description | We study the varieties of reductions associated to the four Severi varieties, the first example of which is the Fano threefold of index 2 and degree 5 studied by Mukai and others. We prove that they are smooth but very special linear sections of Grassmann varieties, and rational Fano manifolds of dimension $3a$ and index $a+1$, for $a=1, 2, 4, 8$. We study their maximal linear spaces and prove that through the general point pass exactly three of them, a result we relate to Cartan's triality principle. We also prove that they are compactifications of affine spaces. | |
| dc.description | 41 pages | |
| dc.identifier | https://arxiv.org/abs/math/0306328 | |
| dc.identifier | http://arxiv.org/abs/math/0306328 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67855 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J45; 14M17; 14N05; 32M15 | |
| dc.title | Severi varieties and their varieties of reductions | |
| dc.type | text |