Curves and vector bundles on quartic threefolds

Abstract

In this paper we study ACM vector bundles $\E$ of rank $k\ge 3$ on hypersurfaces $X_r \subset\Pj^4$ of degree $r\ge 1$. 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 $(c_1,c_2,c_3)$ which may arise in the cases of rank $k=3$ and $k=4$, when $r=4$. For some cases among these we give the corresponding examples, the existence of all the other cases remaining under question.

final version, to apper on JKMS

References in corpus (1)

• A home-made Hartshorne-Serre correspondence

Cited by in corpus (1)

• ACM bundles on cubic surfaces