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arXiv · 1604.00866

ACM sheaves on the double plane

Edoardo Ballico·Sukmoon Huh·Francesco Malaspina·Joan Pons-Llopis
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Abstract

The goal of this paper is to start a study of aCM and Ulrich sheaves on non-integral projective varieties. We show that any aCM vector bundle of rank two on the double plane is a direct sum of line bundles. As a by-product, any aCM vector bundle of rank two on a sufficiently high dimensional quadric hypersurface also splits. We consider aCM and Ulrich vector bundles on a multiple hyperplanes and prove the existence of such bundles that do not split, if the multiple hyperplane is linearly embedded into a sufficiently high dimensional projective space. Then we restrict our attention to the double plane and give a classification of aCM sheaves of rank at most $3/2$ on the double plane and describe the family of isomorphism classes of them.

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Edoardo Ballico, Sukmoon Huh, Francesco Malaspina, Joan Pons-Llopis. 2016-04-04. ACM sheaves on the double plane. https://arxiv.org/abs/1604.00866

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