Splitting of supervector bundles on projective superspaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913655769006080 |
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| author | Almeida, Charles Bruzzo, Ugo |
| author_facet | Almeida, Charles Bruzzo, Ugo |
| contents | We provide a splitting criterion for supervector bundles over the projective superspaces $\mathbb{P}^{n|m}$. More precisely, we prove that a rank $p|q$ supervector bundle on $\mathbb{P}^{n|m}$ with vanishing intermediate cohomology is isomorphic to the direct sum of even and odd line bundles, provided that $n \geq 2$. For $n=1$ we provide an example of a supervector bundle that cannot be written as a sum of line bundles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10765 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Splitting of supervector bundles on projective superspaces Almeida, Charles Bruzzo, Ugo Algebraic Geometry 14M30, 14F06, 14F17 We provide a splitting criterion for supervector bundles over the projective superspaces $\mathbb{P}^{n|m}$. More precisely, we prove that a rank $p|q$ supervector bundle on $\mathbb{P}^{n|m}$ with vanishing intermediate cohomology is isomorphic to the direct sum of even and odd line bundles, provided that $n \geq 2$. For $n=1$ we provide an example of a supervector bundle that cannot be written as a sum of line bundles. |
| title | Splitting of supervector bundles on projective superspaces |
| topic | Algebraic Geometry 14M30, 14F06, 14F17 |
| url | https://arxiv.org/abs/2501.10765 |