Rank 2 ACM bundles on complete intersection Calabi–Yau threefolds

Abstract

The aim of this paper is to classify indecomposable rank two arithmetically Cohen–Macaulay (ACM) bundles on general complete intersection Calabi–Yau threefolds and prove the existence of some of them. New geometric properties of the curves corresponding to rank two ACM bundles (by Serre correspondence) are obtained. These follow from minimal free resolutions of curves in suitably chosen fourfolds (containing Calabi–Yau threefolds as hypersurfaces). A strong indication leading to existence of bundles with \(c_1\,=\,2\), \(c_2\,=\,13\) on a quintic conjectured in Chiantini and Madonna (Le Matematiche 55:239–258, 2000), and Mohan Kumar and Rao (Cent Eur J Math 10(4):1380–1392, 2012) is found.