RANK ONE MAXIMAL COHEN-MACAULAY MODULES OVER SINGULARITIES OF TYPE Y 3

Let R be a hypersurface ring, that is R = S/(f) for a regular local ring (S,m) and0 6= f ∈ m. After Eisenbud [10], any maximal Cohen-Macaulay module has a minimalfree resolution of periodicity 2 which is completely given by a matrix factorization (φ,ψ),φ,ψbeing square matrices over S such that φψ=ψφ= fI

[1]  G. Pfister,et al.  Maximal Cohen–Macaulay modules over the cone of an elliptic curve , 2002 .

[2]  D. Popescu,et al.  Steps in the Classification of Cohen–Macaulay Modules Over Singularities of Type xt + y3 , 1999 .

[3]  Y. Yoshino.  Tensor products of matrix factorizations , 1998, Nagoya Mathematical Journal.

[4]  G. Pfister,et al.  Deformations of maximal Cohen-Macaulay modules , 1996 .

[5]  Mihai Cipu.  An explicit study of l–sequences , 1996 .

[6]  D. Popescu.  Maximal Cohen-Macaulay Modules over Isolated Singularities , 1995 .

[7]  Mihai Cipu,et al.  Ubiquity of relative regular sequences and proper sequences , 1994 .

[8]  J. Herzog,et al.  Indecomposable generalized Cohen-Macaulay modules , 1994 .

[9]  Ø. Solberg,et al.  Liftings and Weak Liftings of Modules , 1993 .

[10]  Mihai Cipu.  Generalized Cohen-Macaulay modules over rings with approximation property , 1991, ANNALI DELL UNIVERSITA DI FERRARA.

[11]  Constantin Kahn.  Reflexive modules on minimally elliptic singularities , 1989 .

[12]  J. Herzog,et al.  On Ulrich-Modules over Hypersurface Rings , 1989 .

[13]  J. Herzog,et al.  Matrix factorizations of homogeneous polynomials , 1988 .

[14]  H. Knörrer.  Cohen-Macaulay modules on hypersurface singularities I , 1987 .

[15]  D. Eisenbud.  On the Resiliency of Determinantal Ideals , 1987 .

[16]  J. Herzog,et al.  Maximal Cohen–Macaulay Modules over Gorenstein Rings and Bourbaki-Sequences , 1987 .

[17]  Michael Atiyah,et al.  Vector Bundles Over an Elliptic Curve , 1957 .