ACM sheaves on the double plane
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 on the double plane and describe the family of isomorphism classes of them.
Cite
@article{arxiv.1604.00866,
title = {ACM sheaves on the double plane},
author = {Edoardo Ballico and Sukmoon Huh and Francesco Malaspina and Joan Pons-Llopis},
journal= {arXiv preprint arXiv:1604.00866},
year = {2018}
}
Comments
33 pages; Major changes in Section 3, 4 and 7; several typos corrected; Comments welcome