\'Etale triviality of finite equivariant vector bundles
Keyword(s):
Let H be a complex Lie group acting holomorphically on a complex analytic space X such that the restriction to X_{\mathrm{red}} of every H-invariant regular function on X is constant. We prove that an H-equivariant holomorphic vector bundle E over X is $H$-finite, meaning f_1(E)= f_2(E) as H-equivariant bundles for two distinct polynomials f_1 and f_2 whose coefficients are nonnegative integers, if and only if the pullback of E along some H-equivariant finite \'etale covering of X is trivial as an H-equivariant bundle.
2011 ◽
Vol 08
(07)
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pp. 1433-1438
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1976 ◽
Vol 61
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pp. 197-202
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2004 ◽
Vol 134
(1)
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pp. 33-38
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2000 ◽
Vol 11
(01)
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pp. 29-40
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2015 ◽
Vol 2015
(706)
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