Embeddings of homogeneous spaces in prime characteristics
| dc.creator | Lauritzen, Niels | |
| dc.date | 1995-02-16 | |
| dc.date.accessioned | 2026-07-07T09:06:22Z | |
| dc.date.available | 2026-07-07T09:06:22Z | |
| dc.description | Let $G$ be a reductive linear algebraic group. The simplest example of a projective homogeneous $G$-variety in characteristic $p$, not isomorphic to a flag variety, is the divisor $x_0 y_0^p+x_1 y_1^p+x_2 y_2^p=0$ in $P^2\times P^2$, which is $SL_3$ modulo a non-reduced stabilizer containing the upper triangular matrices. In this paper embeddings of projective homogeneous spaces viewed as $G/H$, where $H$ is any subgroup scheme containing a Borel subgroup, are studied. We prove that $G/H$ can be identified with the orbit of the highest weight line in the projective space over the simple $G$-representation $L(λ)$ of a certain highest weight $λ$. This leads to some strange embeddings especially in characteristic $2$, where we give an example in the $C_4$-case lying on the boundary of Hartshorne's conjecture on complete intersections. Finally we prove that ample line bundles on $G/H$ are very ample. This gives a counterexample to Kodaira type vanishing with a very ample line bundle, answering an old question of Raynaud. | |
| dc.description | 10 pages, AMS-LaTeX | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9502016 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9502016 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149981 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Embeddings of homogeneous spaces in prime characteristics | |
| dc.type | text |