Étale triviality of finite equivariant vector bundles
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866909422445395968 |
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| author | Biswas, Indranil O'Sullivan, Peter |
| author_facet | Biswas, Indranil O'Sullivan, Peter |
| contents | 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 étale covering of X is trivial as an H-equivariant bundle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_06491 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Étale triviality of finite equivariant vector bundles Biswas, Indranil O'Sullivan, Peter Algebraic Geometry Category Theory 32L10, 53C55, 14D21, 16B50 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 étale covering of X is trivial as an H-equivariant bundle. |
| title | Étale triviality of finite equivariant vector bundles |
| topic | Algebraic Geometry Category Theory 32L10, 53C55, 14D21, 16B50 |
| url | https://arxiv.org/abs/2103.06491 |