Exploring the interplay of semistable vector bundles and their restrictions on reducible curves
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912194628681728 |
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| author | N., Suhas B. Roy, Praveen Kumar Singh, Amit Kumar |
| author_facet | N., Suhas B. Roy, Praveen Kumar Singh, Amit Kumar |
| contents | Let $C$ be a comb-like curve over $\mathbb{C}$, and $E$ be a vector bundle of rank $n$ on $C$. In this paper, we investigate the criteria for the semistability of the restriction of $E$ onto the components of $C$ when $E$ is given to be semistable with respect to a polarization $w$. As an application, assuming each irreducible component of $C$ is general in its moduli space, we investigate the $w$-semistability of kernel bundles on such curves, extending the results (completely for rank two and partially for higher rank) known in the case of a reducible nodal curve with two smooth components, but here, using different techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11356 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exploring the interplay of semistable vector bundles and their restrictions on reducible curves N., Suhas B. Roy, Praveen Kumar Singh, Amit Kumar Algebraic Geometry 14H60 Let $C$ be a comb-like curve over $\mathbb{C}$, and $E$ be a vector bundle of rank $n$ on $C$. In this paper, we investigate the criteria for the semistability of the restriction of $E$ onto the components of $C$ when $E$ is given to be semistable with respect to a polarization $w$. As an application, assuming each irreducible component of $C$ is general in its moduli space, we investigate the $w$-semistability of kernel bundles on such curves, extending the results (completely for rank two and partially for higher rank) known in the case of a reducible nodal curve with two smooth components, but here, using different techniques. |
| title | Exploring the interplay of semistable vector bundles and their restrictions on reducible curves |
| topic | Algebraic Geometry 14H60 |
| url | https://arxiv.org/abs/2501.11356 |