Homogeneous ACM bundles on Grassmannians of exceptional types

Abstract

In this paper, we characterize homogeneous arithmetically Cohen-Macaulay (ACM) bundles over homogeneous varieties of Picard rank one in terms of their associated data. This is a generalization of the result on homogeneous varieties of Picard rank one of classical types presented by Costa and Miró-Roig for type A, and Du, Fang, and Ren for types $B,C$ and D. We show that there are only finitely many irreducible homogeneous ACM bundles by twisting line bundles over Grassmannians of exceptional types. As a consequence, we prove that some Grassmannians of exceptional types are of wild representation type.