Vector bundles on a three dimensional neighborhood of a ruled surface

2001/10/23 by Edoardo Ballico, Ballico, Edoardo, Elizabeth Gasparim +1
Mathematics · #14J60 #32G08 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG #msc:14J60 #msc:32G08

paper · pdf · doi:10.48550/arxiv.math/0110258

Revised version to appear in J. Pure Appl. Algebra. A new section on deformations was added

openalex publication_date 2001/10/23 · arxiv created 2004/05/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S be a ruled surface inside a smooth threefold W and let E be a vector bundle on a formal neighborhood of S. We find minimal conditions under which the local moduli space of E is finite dimensional and smooth. Moreover, we show that E is a flat limit of a flat family of vector bundles whose general element we describe explicitly.

Citations

• Ample Subvarieties of Algebraic Varieties

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