An example of a stable but fibrewise nonstable bundle on the twistor space of a hyperk\"ahler manifold

Artour Tomberg

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arXiv · 1812.11860

An example of a stable but fibrewise nonstable bundle on the twistor space of a hyperk\"ahler manifold

Artour Tomberg

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Abstract

We construct an explicit example of a stable bundle on the twistor space $\mathrm{Tw}(M)$ of a hyperk\"ahler manifold $M$ whose restrictions to all the fibres of the natural twistor projection $\pi : \mathrm{Tw}(M) \to \mathbb{CP}^1$ are nonstable. We also describe the relationship between bundles on $\mathrm{Tw}(M)$ that do not have subsheaves of strictly lower rank and bundles that stably restrict to the fibres of $\pi$, and announce a result whose proof will appear in a forthcoming paper.

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BibTeX RIS

Artour Tomberg. 2018-12-31. An example of a stable but fibrewise nonstable bundle on the twistor space of a hyperk\"ahler manifold. https://arxiv.org/abs/1812.11860

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