Transformation Groups

, Volume 20, Issue 4, pp 1043–1073 | Cite as




Let X be a T-variety, where T is an algebraic torus. We describe a fully faithful functor from the category of T-equivariant vector bundles on X to a certain category of filtered vector bundles on a suitable quotient of X by T. We show that if X is factorial, this functor gives an equivalence of categories. This generalizes Klyachko's description of equivariant vector bundles on toric varieties. We apply our machinery to show that vector bundles of low rank on ℙ n which are equivariant with respect to special subtori of the maximal torus must split, generalizing a theorem of Kaneyama. Further applications include descriptions of global vector fields on T-varieties, and a study of equivariant deformations of equivariant vector bundles.


Exact Sequence Vector Bundle Line Bundle Tangent Bundle Algebraic Torus 
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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada
  2. 2.School of MathematicsThe University of ManchesterManchesterUK

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