A remark on a theorem of Narasimhan and Ramanan
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916494037745664 |
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| author | Pine, Jagadish |
| author_facet | Pine, Jagadish |
| contents | In this short note, we provide an alternative proof of a notable theorem by Narasimhan and Ramanan. The theorem states that the moduli space of $S$-equivalence classes of semistable rank $2$ vector bundles over a curve $X$ of genus $2$ with trivial determinant is isomorphic to $\mathbb{P}^3$. Our proof relies on a criterion by Bauer and Szemberg, which characterizes projective spaces among smooth Fano varieties using Seshadri constants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15774 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A remark on a theorem of Narasimhan and Ramanan Pine, Jagadish Algebraic Geometry 14C20, 14H60, 14F05 In this short note, we provide an alternative proof of a notable theorem by Narasimhan and Ramanan. The theorem states that the moduli space of $S$-equivalence classes of semistable rank $2$ vector bundles over a curve $X$ of genus $2$ with trivial determinant is isomorphic to $\mathbb{P}^3$. Our proof relies on a criterion by Bauer and Szemberg, which characterizes projective spaces among smooth Fano varieties using Seshadri constants. |
| title | A remark on a theorem of Narasimhan and Ramanan |
| topic | Algebraic Geometry 14C20, 14H60, 14F05 |
| url | https://arxiv.org/abs/2411.15774 |