AI 中文总结
研究维数至少为\(2\)且皮卡秩为\(1\)的光滑射影簇上合冲丛稳定性，证明在此类簇上丰富线丛合冲丛稳定，尤其适用于射影空间完全交，扩展了前人成果。
AI 中文摘要
若\(X\)是维数至少为\(2\)且皮卡秩为\(1\)的光滑射影簇，其上每个丰富线丛都是整体生成的，我们证明了任何丰富线丛的合冲丛是稳定的。这尤其适用于射影空间中的完全交。此结果扩展了蒋仁、科安达等人的早期成果。
英文摘要
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.
