Globally generated vector bundles on a smooth quadric surface

2013/12/09 by Edoardo Ballico, Ballico, Edoardo, Sukmoon Huh +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG

paper · pdf · doi:10.48550/arxiv.1312.2472

23 pages; Comments welcome; Several corrections

openalex publication_date 2013/12/09 · arxiv created 2014/06/13 · arxiv updated 2014/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give the classification of globally generated vector bundles of rank 2 on a smooth quadric surface with c₁≤ (2,2) in terms of the indices of the bundles, and extend the result to arbitrary higher rank case. We also investigate their indecomposability and give the sufficient and necessary condition on numeric data of vector bundles for indecomposability.

Citations

• Rank two globally generated vector bundles with c₁ ≤ 5

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