Graded CM modules over graded normal CM domains (Q2367483)

Maximal Cohen Macaulay (CM) modules over Henselian Cohen-Macaulay rings have been studied quite extensively in the past. In this paper the authors turn to graded CM modules over a graded normal CM domain. Because methods used in the Henselian cases, though probably feasible in some cases here, would involve hard computation, a new method is proposed for the classification of the graded CM modules. This new method utilizes Demazure's description for a graded ring \(R\) as starting point; the preliminary part of the paper is devoted to results concerning this description which are to be used repeatedly later on. Other aspects which are used are an order defined with respect to some of the parameters in Demazure's description, equivalence between certain categories of syzygies and vector bundles. Especially interesting results are obtained for the case where \(X\) \((=\text{Proj} (R))\) is a curve. One of the main results, in rough terms, states that when \(X\) is a curve, any CM module over \(R\) is obtained as an ``extension'' of a vector bundle over \(X\) by a representation of a certain quiver.