Geometry and Moduli Space of Certain Rank-4 Vector Bundles on \mathbb P⁴

2000/11/20 by Alexander Getmanenko, Getmanenko, Alexander
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Polynomial and algebraic computation #math.AG

paper · pdf · doi:10.48550/arxiv.math/0011147

54 pages, Latex

arxiv created 2000/11/20 · openalex publication_date 2000/11/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Mathematical instanton bundles of rank 4 and c₂=2 on \mathbb P⁴ have a smoothquasiprojective moduli space, which is shown via a direct GIT construction. A complete classification of jumping lines of these vector bundles is obtained. The duals of these bundles are described. Dimension computations and irreducibility proofs for some "interesting" subsets of the moduli space are presented. Restrictions of vector bundles from \mathbb P⁴ to \mathbb P³ are shown to produce mathematical instanton bundles on \mathbb P³.

Citations

• Construction of instantons

Related

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• On the rationality of the moduli space of instanton bundles on the projective 3-space
• Rationality and categorical properties of the moduli of instanton bundles on the projective 3-space
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• Moduli Spaces of Instantons on Noncommutative 4-Manifolds II