Vector bundles on Hirzebruch surfaces whose twists by a non-ample line bundle have natural cohomology

2007/10/18 by Edoardo Ballico, Ballico, E., Francesco Malaspina +1
Mathematics · #14J60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0710.3494

openalex publication_date 2007/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Here we study vector bundles E on the Hirzebruch surface F_e such that their twists by a spanned, but not ample, line bundle M = \mathcal O_Fe(h+ef) have natural cohomology, i.e. h⁰(F_e,E(tM)) >0 implies h¹(F_e,E(tM)) = 0.

Citations

• Algebraic Families on an Algebraic Surface

Related

• A cohomological splitting criterion for rank 2 vector bundles on Hirzebruch surfaces
• Special Ulrich bundles on non-special surfaces with p_g=q=0
• On families of rank-2 uniform bundles on Hirzebruch surfaces and Hilbert schemes of their scrolls
• Twisted Kodaira-Spencer classes and the geometry of surfaces of general type
• Brill-Noether theorems and globally generated vector bundles on Hirzebruch surfaces