On Stable Bundles of Ranks 2 and 3 on P³

2003/10/06 by Al Vitter, Vitter, Al · 1 citation
Mathematics · #14F05 #14J60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:14F05 #msc:14J60

paper · pdf · doi:10.48550/arxiv.math/0310073

35 pages,AMSLaTeX

arxiv created 2003/10/06 · openalex publication_date 2003/10/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study rank 3 stable bundles E on P³ as extensions of a line bundle B on a smooth surface S in P³ by the direct sum of three copies of O_P³(-ν). In most cases, S (the dependency locus of three sections of E(ν)) lies in the Noether-Lefschetz locus. We give a detailed analysis when S contains a line L and B is constructed from divisors of the form aL+bC for H=L+C a hyperplane section of S. We study the parameter space of this construction and compare it to the full (Gieseker-Maruyama) moduli space. We also analyse the case when B is a power of the hyperplane bundle. The same approach is used to study rank 2 bundles on P³.

Cited by

• Moduli spaces of stable bundles on ruled 3-folds and Brill-Noether problems

Related

• Stable rank 3 vector bundles on ℙ³ with c₁ = 0, c₂ = 3
• Rank-3 stable bundles on rational ruled surfaces
• The irreducibility of the moduli space of stable vector bundles of rank 2 on a quintic in \pp³
• Stability of Rank 2 Ulrich Bundles on Projective K3 Surfaces
• Construction of stable rank 2 vector bundles on ℙ³ via symplectic bundles