Rank 3 arithmetically Cohen-Macaulay bundles on hypersurfaces

2015/06/10 by Tripathi, Amit · 1 citation
#14J60 (Secondary) #14J70 (Primary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1506.03165

Abstract

Let X be a smooth projective hypersurface of dimension ≥ 5 and let E be an arithmetically Cohen-Macaulay bundle on X of any rank. We prove that E splits as a direct sum of line bundles if and only if Hⁱ_*(X, \wedge² E) = 0 for i = 1,2,3,4. As a corollary this result proves a conjecture of Buchweitz, Greuel and Schreyer for the case of rank 3 arithmetically Cohen-Macaulay bundles.

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• Extendable codimension two subvarieties in a general hypersurface

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