On Buchsbaum bundles on quadric hypersurfaces

2011/07/30 by Edoardo Ballico, Ballico, Edoardo, Francesco Malaspina +5 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14F05

paper · pdf · doi:10.48550/arxiv.1108.0075

22 pages, no figure

arxiv created 2011/07/30 · arxiv updated 2011/08/02

Abstract

Let E be an indecomposable rank two vector bundle on the projective space \PPⁿ, n ≥ 3, over an algebraically closed field of characteristic zero. It is well known that E is arithmetically Buchsbaum if and only if n=3 and E is a null-correlation bundle. In the present paper we establish an analogous result for rank two indecomposable arithmetically Buchsbaum vector bundles on the smooth quadric hypersurface Q_n⊂\PPⁿ⁺¹, n≥ 3. We give in fact a full classification and prove that n must be at most 5. As to k-Buchsbaum rank two vector bundles on Q₃, k≥2, we prove two boundedness results.

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