2026/07/12 by Supravat Sarkar
Mathematics · #math.AG
If X is a smooth projective variety of dimension ≥ 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, Coandă and others. We also show that in any dimension ≥ 2, there is a smooth projective variety of Picard rank 1 with an unstable syzygy bundle. This completely answers a question of Fulger-Langer.