On the Local Cohomology of Reflexive Modules of Rank One over Normal   Semigroup Rings
  In this work we describe the local cohomology of reflexive modules of rank one over normal semigroup rings with respect to monomial ideals. Using our description we show that the problem of classifying maximal Cohen-Macaulay modules of rank one can be rephrased in terms of finding integral solutions to certain sets of linear inequalities. 
Markus Perling