Abstract
Let T be a complex torus acting algebraically on ℙ1(ℂ). In this note we prove a T-equivariant analogue of a theorem of Grothendieck. More specifically, we show that any T-equivariant vector bundle on ℙ1(ℂ) is a direct sum of T-equivariant line subbundles.
To Professor C.S. Seshadri on his seventieth birthday
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References
Grothendieck, A.: Sur la classification des fibres holomorphes sur la sphere de Riemann, Amer. J. Math. 79 (1957), 121–138.
Hartshorne, R.: Algebraic Geometry, GTM 52, Springer-Verlag, 1977.
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© 2003 Hindustan Book Agency
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Kumar, S. (2003). Equivariant Analogue of Grothendieck’s Theorem for Vector Bundles on ℙ1 . In: Lakshmibai, V., et al. A Tribute to C. S. Seshadri. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-11-8_29
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DOI: https://doi.org/10.1007/978-93-86279-11-8_29
Publisher Name: Hindustan Book Agency, Gurgaon
Print ISBN: 978-81-85931-39-5
Online ISBN: 978-93-86279-11-8
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