Journal of the
Korean Mathematical Society JKMS

In this paper we study arithmetically Cohen-Macaulay (ACM for short) vector bundles $\mathcal E$ of rank $k \geq 3$ on hypersurfaces $X_r \subset\mathbb P^4$ of degree $r \geq 1$. 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 $\mathcal E$ we derive a list of possible Chern classes $(c_1,c_2,c_3)$ which may arise in the cases of rank $k=3$ and $k=4$, when $r=4$ and we give several examples.

Keywords: quartic threefold, ACM bundle, projectively normal curve

MSC numbers: 14J60