On invariant rank two vector bundles on $\mathbb{P}^2$
In this paper we characterize the rank two vector bundles on $\mathbb{P}^2$ which are invariant under the actions of the parabolic subgroups $G_p:=\operatorname{Stab}_p(\mathrm{PGL}(3))$ fixing a point in the projective plane, $G_L:=\operatorname{Stab}_L(\mathrm{PGL}(3))$ fixing a line, and when $p...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/195360 |
| Acceso en línea: | https://hdl.handle.net/2445/195360 |
| Access Level: | acceso abierto |
| Palabra clave: | Geometria algebraica Homologia Grups algebraics lineals Algebraic geometry Homology Linear algebraic groups |
| Sumario: | In this paper we characterize the rank two vector bundles on $\mathbb{P}^2$ which are invariant under the actions of the parabolic subgroups $G_p:=\operatorname{Stab}_p(\mathrm{PGL}(3))$ fixing a point in the projective plane, $G_L:=\operatorname{Stab}_L(\mathrm{PGL}(3))$ fixing a line, and when $p \in L$, the Borel subgroup $\mathbf{B}=G_p \cap G_L$ of PGL(3). Moreover, we prove that the geometrical configuration of the jumping locus induced by the invariance does not, on the other hand, characterize the invariance itself. Indeed, we find infinite families that are almost uniform but not almost homogeneous. |
|---|