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arXiv · 2607.10585

Stable and unstable syzygy bundles on certain Picard rank one varieties

Supravat Sarkar
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Abstract

If $X$ is a smooth projective variety of dimension $\geq 2$ and Picard rank $1$ on which every ample line bundle has at least $2$ linearly independent sections, we prove that syzygy bundle of any nontrivial globally generated line bundle is stable. We apply this to show stability of syzygy bundles in non-general type complete intersections in weighted projective spaces, and all complete intersections in projective spaces. This extends earlier results of Jiang-Ren, Coand{ă} and others. We also show that in any dimension $\geq 2$, there is a smooth projective variety of Picard rank $1$ with an unstable syzygy bundle. This completely answers a question of Fulger-Langer.

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Supravat Sarkar. 2026-07-21. Stable and unstable syzygy bundles on certain Picard rank one varieties. https://arxiv.org/abs/2607.10585

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