Schémas de Fano
| dc.creator | Debarre, O. | |
| dc.creator | Manivel, L. | |
| dc.date | 1996-11-26 | |
| dc.date.accessioned | 2026-07-07T09:07:06Z | |
| dc.date.available | 2026-07-07T09:07:06Z | |
| dc.description | Let X be a subvariety of $P^n$ defined by equations of degrees $ d =(d_1,...,d_s)$, over an algebraically closed field k of any characteristic. We study properties of the Fano scheme $F_r(X)$ that parametrizes linear subspaces of dimension r contained in X. We prove that $F_r(X)$ is connected and smooth of the expected dimension for n big enough (this was previously known in characteristic 0 or for r=1). Using Bott's theorem, we prove a vanishing theorem for certain bundles on the Grassmannian and use it to calculate the cohomology groups of $F_r(X)$ in degree $\le \dim X-2r$, and to prove that $F_r(X)$ is projectively normal in the Grassmannian. Finally, we prove that for n big enough, the rational Chow group $A_1(F_r(X))$ is of rank 1, and $F_r(X)$ is unirational. All bounds on n are effective. | |
| dc.description | PlainTeX v 1.2, 22 pages, in French. Run it twice to get cross-references right | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9611033 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9611033 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150248 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Schémas de Fano | |
| dc.type | text |