2010/01/31 by Tokuji Araya, Araya, Tokuji, Kei-ichiro Iima +3
Mathematics · #Commutative Algebra and Its Applications #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.1002.0137
Let R be a complete local hypersurface over an algebraically closed field of characteristic different from two, and suppose that R has countable Cohen-Macaulay representation type. In this paper, it is proved that the maximal Cohen-Macaulay R-modules which are locally free on the punctured spectrum are dominated by the maximal Cohen-Macaulay R-modules which are not locally free on the punctured spectrum. More precisely, there exists a single R-module X such that the indecomposable maximal Cohen-Macaulay R-modules not locally free on the punctured spectrum are X and its syzygy ΩX and that any other maximal Cohen-Macaulay R-module is obtained from some extension of X and ΩX.