On the equivariant vector bundles on $\mathbb{CP}^1$
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918081194885120 |
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| author | Biswas, Indranil Kumar, Manish Parameswaran, A. J. |
| author_facet | Biswas, Indranil Kumar, Manish Parameswaran, A. J. |
| contents | Let $H$ be a subgroup of ${\rm PGL}(2,\mathbb C)$ (respectively, ${\rm SL}(2,\mathbb C)$) such that the Zariski closure in ${\rm PGL}(2,\mathbb C)$ (respectively, ${\rm SL}(2,\mathbb C)$) of some compact subgroup of $H$ contains $H$. We classify the $H$--equivariant holomorphic vector bundles on $\mathbb{CP}^1$. This generalizes \cite{BM} where $H$ was assumed to be a finite abelian group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02359 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the equivariant vector bundles on $\mathbb{CP}^1$ Biswas, Indranil Kumar, Manish Parameswaran, A. J. Algebraic Geometry Let $H$ be a subgroup of ${\rm PGL}(2,\mathbb C)$ (respectively, ${\rm SL}(2,\mathbb C)$) such that the Zariski closure in ${\rm PGL}(2,\mathbb C)$ (respectively, ${\rm SL}(2,\mathbb C)$) of some compact subgroup of $H$ contains $H$. We classify the $H$--equivariant holomorphic vector bundles on $\mathbb{CP}^1$. This generalizes \cite{BM} where $H$ was assumed to be a finite abelian group. |
| title | On the equivariant vector bundles on $\mathbb{CP}^1$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2507.02359 |