On automorphism groups of fiber bundles

2010/12/21 by Michel Brion, Brion, Michel · 2 citations
Mathematics · Physics and Astronomy · #14L10 #14L15 #14L30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1012.4606

openalex publication_date 2010/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain analogues of classical results on automorphism groups of holomorphic fiber bundles, in the setting of group schemes. Also, we establish a lifting property of the connected automorphism group, for torsors under abelian varieties. These results will be applied to the study of homogeneous bundles over abelian varieties.

Citations

• Homogeneous bundles over abelian varieties

Cited by

• On the GIT quotient of Grassmannians by one dimensional torus
• The dual Lagrangian fibration of known hyper-Kähler manifolds

Related

• Homogeneous bundles over abelian varieties
• Abelian varieties as automorphism groups of smooth projective varieties in arbitrary characteristics
• A remark on the structure of torsors under an affine group scheme
• Automorphism groups of affine varieties and their Lie algebras
• Homogeneous spaces over an abelian variety