Severi varieties
| dc.creator | Chaput, P. E. | |
| dc.date | 2001-02-06 | |
| dc.date | 2001-02-07 | |
| dc.date.accessioned | 2026-07-07T04:40:00Z | |
| dc.date.available | 2026-07-07T04:40:00Z | |
| dc.description | R. Hartshorne conjectured and F. Zak proved that any n-dimensional smooth non-degenerate complex algebraic variety X in a m-dimensional projective space P satisfies Sec(X)=P if m<3n/2+2. In this article, I deal with the limiting case of this theorem, namely the Severi varieties, defined by the conditions m=3n/2+2 and Sec(X) different from P. I want to give a different proof of a theorem of F. Zak classifying all Severi varieties: I will prove that any Severi variety is homogeneous and then deduce their classification and the following geometric property : the derivatives of the equation of Sec(X), which is a cubic hypersurface, determine a birational morphism of P. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0102042 | |
| dc.identifier | http://arxiv.org/abs/math/0102042 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60897 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14M07; 14M17; 14E07 | |
| dc.title | Severi varieties | |
| dc.type | text |