Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/195360
Title: | On invariant rank two vector bundles on $\mathbb{P}^2$ |
Author: | Marchesi, Simone Vallès, Jean |
Keywords: | Geometria algebraica Homologia Grups algebraics lineals Algebraic geometry Homology Linear algebraic groups |
Issue Date: | 2023 |
Publisher: | Universitat Autònoma de Barcelona |
Abstract: | 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. |
Note: | Reproducció del document publicat a: https://doi.org/10.5565/PUBLMAT6712306 |
It is part of: | Publicacions Matemàtiques, 2023, vol. 67, p. 259-275 |
URI: | http://hdl.handle.net/2445/195360 |
Related resource: | https://doi.org/10.5565/PUBLMAT6712306 |
ISSN: | 0214-1493 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
732370.pdf | 382.12 kB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.