On uniform and nonhomogeneous vector bundles over Grassmannians

2024/04/03 by Rong Du, Du, Rong, Wang, Yiting +2
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2404.02593

openalex publication_date 2024/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We demonstrate the existence of a uniform and nonhomogeneous vector bundle E of rank (n-d)(m+1)-1 over Grassmannian \mathbbG(d,n), where m>d and 1≤ d ≤ n-d-1 with a ℙ-homogeneity degree h(E)=d. Particularly, we establish an upper bound of 3(n-d)-2 for the uniform-homogeneous shreshold of \mathbbG(d,n). Additionally, we construct indecomposable uniform vector bundles of rank (d+2)(n-d)+d-2+∑_i=0^p\tbinomd-1+p-ip-i(1+i)-\tbinomp+dp that are nonhomogeneous over \mathbbG(d,n).

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