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arXiv · 2604.20264

Asymptotically Z-stable bundles over projective surfaces

Luiz Lara·Henrique N. Sá Earp
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Abstract

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 $\mu$-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.

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Luiz Lara, Henrique N. Sá Earp. 2026-04-22. Asymptotically Z-stable bundles over projective surfaces. https://arxiv.org/abs/2604.20264

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