Stability of Kernel Bundles
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929488860807168 |
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| author | Song, Chen |
| author_facet | Song, Chen |
| contents | In this paper, we study the stability of general kernel bundles on $\mathbb{P}^n$. Let $a,b,d>0$ be integers. A kernel bundle $E_{a,b}$ on $\mathbb{P}^n$ is defined as the kernel of a surjective map $ϕ:\mathcal{O}_{\mathbb{P}^n}(-d)^a\rightarrow \mathcal{O}_{\mathbb{P}^n}^b$. Here $ϕ$ is represented by a $b\times a$ matrix $(f_{ij})$ where the entries $f_{ij}$ are polynomials of degree $d$. We give sufficient conditions for semistability of a general kernel bundle on $\mathbb{P}^n$, in terms of its Chern class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03586 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of Kernel Bundles Song, Chen Algebraic Geometry In this paper, we study the stability of general kernel bundles on $\mathbb{P}^n$. Let $a,b,d>0$ be integers. A kernel bundle $E_{a,b}$ on $\mathbb{P}^n$ is defined as the kernel of a surjective map $ϕ:\mathcal{O}_{\mathbb{P}^n}(-d)^a\rightarrow \mathcal{O}_{\mathbb{P}^n}^b$. Here $ϕ$ is represented by a $b\times a$ matrix $(f_{ij})$ where the entries $f_{ij}$ are polynomials of degree $d$. We give sufficient conditions for semistability of a general kernel bundle on $\mathbb{P}^n$, in terms of its Chern class. |
| title | Stability of Kernel Bundles |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2401.03586 |