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Title: On invariant rank two vector bundles on $\mathbb{P}^2$
Author: Marchesi, Simone
Vallès, Jean
Keywords: Geometria algebraica
Grups algebraics lineals
Algebraic geometry
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.
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It is part of: Publicacions Matemàtiques, 2023, vol. 67, p. 259-275
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ISSN: 0214-1493
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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