Let A= k [[zl,..., zr]\be the formal power series ring in the variables z, over a field k, and let f= f
(zx,..., zr) be a non-zero non-unit in A. Then we call R= A/{f) the local ring of/In [19] Knorrer …

0.1. H. Kn/Srrer [Kn6] showed the following property of the local ring R of an isolated simple
hypersurface singularity: There are only finitely many isomorphism classes of …

In the last few years the maximal Cohen-Macaulay modules over local rings of singularities
have been studied by methods of representation theory, commutative algebra, and algebraic …

Let R be an integrally closed complete local commutative noetherian Cohen-Macaulay
domain with maximal ideal m and R/m= k an algebraically closed field. We abbreviate …

Let K be a field, K [[x]] the formal power series ring in the variables x= x1,..., xn, K [[y]] the
formal power series ring in the variables y= y1,..., ym, f∈ K [[x]] and g∈ K [[y]] two non-zero …

Throughout this note R is an equidimensional commutative Gorenstein ring and A is an R-
algebra which is a finitely generated (maximal) Cohen-Macaulay R-module. We denote by …

Let (R, m) be a complete Cohen-Macaulay isolated singularity over a field/(which is either
perfect or [/{: f {Pj< oo if p:= char/{> 0. According to Dieterich [Di] and [Yo] Ch. 6 (see also …

I include a complete proof of this result in this survey article. My emphasis lies on the
conscruction of maximal Cohen-Macaulay modules via matrix factorizations (section 2), from …

Let f (X)= f (X0..... Xd) be a polynomial in C [X0..... Xd], such that the hypersufface H c
Ad+~(C) given by f (X) has an isolated singularity at 0, and let A=~,. 0= C [[Xo..... Xd]]/(f (X)) …

Let R be a reduced local Noetherian ring of dimension one, and assume that the integral
closure/~ is finitely generated as an R-module. The main theorem of [13] gives necessary …