Curves and vector bundles on quartic threefolds

Abstract

In this paper we study arithmetically Cohen-Macaulay (ACM for short) vector bundles E of rank k 3 on hypersurfaces Xr P4 of degree r 1. We consider here mainly the case of degree r = 4, which is the first unknown case in literature. Under some natural conditions for the bundle E we derive a list of possible Chern classes (c1, c2, c3) which may arise in the cases of rank k = 3 and k = 4, when r = 4 and we give several examples.