Vector Bundles and Cohen-Macaulay Modules

摘要

The aim of this survey is to present recent results on classification of vector bundles over projective curves and Cohen-Macaulay modules over surface singularities, mainly obtained by the author in collaboration with G.-M. Greuel and I. Kashuba [DG3, DGK]. We consider this problem from the viewpoint of the representation theory, being mainly interested in the representation type (finite, tame or wild) and, for tame case, in the description of all objects. So we do not deal with stable bundles and related topics, though something can be done in this direction too (cf. Section 4). We mostly consider algebras and varieties over an algebraically closed field k, though some results remain valid in a more general setting.