Stability of Kernel Bundles

2024/01/07 by Chen Song, Song, Chen
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2401.03586

openalex publication_date 2024/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the stability of general kernel bundles on ℙn. Let a,b,d>0 be integers. A kernel bundle Ea,b on ℙn is defined as the kernel of a surjective map ϕ:Oℙn(-d)a→ Oℙnb. Here ϕ is represented by a b× a matrix (fij) where the entries fij are polynomials of degree d. We give sufficient conditions for semistability of a general kernel bundle on ℙn, in terms of its Chern class.

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