A Cohomological criterion for the splitting of vector bundles on ℙ^n₁×⋯×ℙ^n_s

2025/11/27 by Damian Maingi, Maingi, Damian
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2511.22543

Abstract

In this paper we study the cohomological criterion for the splitting of vector bundles on multiprojective spaces ℙ^n₁×…×ℙ^n_s. We also give a generalization of vanishing cohomological criteria for vector bundles on ℙⁿ×…×ℙⁿ.

Citations

• Syzygy Theoretic Approach to Horrocks-type Criteria for Vector Bundles
• Cohomological Characterization of Vector Bundles on Grassmannians of Lines
• Regularity and Cohomological Splitting Conditions for Vector Bundles on\n Multiprojective Spaces
• Qregularity and an Extension of Evans-Griffiths Criterion to Vector Bundles on Quadrics
• m-blocks collections and Castelnuovo-Mumford regularity in multiprojective spaces
• Castelnuovo-Mumford Regularity in Biprojective Spaces

Related

• Cohomological splitting conditions of vector bundles on ℙ^n₁×⋯×ℙ^n_s
• Regularity and Cohomological Splitting Conditions for Vector Bundles on\n Multiprojective Spaces
• A Few Splitting Criteria for Vector Bundles
• A splitting criterion for vector bundles on blowing ups of the plane
• Splitting of supervector bundles on projective superspaces