Asymptotically Z-stable bundles over projective surfaces
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915948711116800 |
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| author | Lara, Luiz Earp, Henrique N. Sá |
| author_facet | Lara, Luiz Earp, Henrique N. Sá |
| contents | We study the existence of asymptotically $Z$-stable (a.Z stable) bundles over polycyclic surfaces. Our choice of polynomial central charge is related to the existence of solutions of the deformed Hermitian--Yang--Mills equations, with vanishing $B$-field, in the large-volume limit. The main result is a technique to construct rank $3$, strictly a.Z-stable bundles as extensions of a line bundle by a $μ$-stable bundle of rank $2$. In particular, this leads to new examples of strictly a.Z-stable bundles over $\mathbb{P}^2$, the product $\mathbb{P}^1\times \mathbb{P}^1$, and the blow-up $\mathrm{Bl}_q\mathbb{P}^2$. We also present an analogue of the Hoppe criterion for the a.Z-stability of vector bundles of rank $2$, which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20264 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotically Z-stable bundles over projective surfaces Lara, Luiz Earp, Henrique N. Sá Algebraic Geometry 14960 (Primary) 53C07 (Secondary) We study the existence of asymptotically $Z$-stable (a.Z stable) bundles over polycyclic surfaces. Our choice of polynomial central charge is related to the existence of solutions of the deformed Hermitian--Yang--Mills equations, with vanishing $B$-field, in the large-volume limit. The main result is a technique to construct rank $3$, strictly a.Z-stable bundles as extensions of a line bundle by a $μ$-stable bundle of rank $2$. In particular, this leads to new examples of strictly a.Z-stable bundles over $\mathbb{P}^2$, the product $\mathbb{P}^1\times \mathbb{P}^1$, and the blow-up $\mathrm{Bl}_q\mathbb{P}^2$. We also present an analogue of the Hoppe criterion for the a.Z-stability of vector bundles of rank $2$, which may be of independent interest. |
| title | Asymptotically Z-stable bundles over projective surfaces |
| topic | Algebraic Geometry 14960 (Primary) 53C07 (Secondary) |
| url | https://arxiv.org/abs/2604.20264 |