The cone spanned by maximal Cohen-Macaulay modules and an application

Maximal Cohen-macaulay Modules over Hypersurface Rings

This paper is a brief survey on various methods to classify maximal Cohen-Macaulay modules over hypersurface rings. The survey focuses on the contributions in this topic of Dorin Popescu together with his collaborators.

Rank One Maximal Cohen-macaulay Modules Over

Maximal Cohen-Macaulay Modules over the Affine Cone of the Simple Node

A concrete description of all graded maximal Cohen–Macaulay modules of rank one and two over the non-isolated singularities of type y3 1 +y 2 1y3−y 2y3 is given. For this purpose we construct an alghoritm that provides extensions of MCM modules over an arbitrary hypersurface.

Liaison with Cohen–Macaulay modules

We describe some recent work concerning Gorenstein liaison of codimension two subschemes of a projective variety. Applications make use of the algebraic theory of maximal Cohen–Macaulay modules, which we review in an Appendix.

RESULTS ON ALMOST COHEN-MACAULAY MODULES

Let $(R,underline{m})$ be a commutative Noetherian local ring and $M$ be a non-zero finitely generated $R$-module. We show that if $R$ is almost Cohen-Macaulay and $M$ is perfect with finite projective dimension, then $M$ is an almost Cohen-Macaulay module. Also, we give some necessary and sufficient condition on $M$ to be an almost Cohen-Macaulay module, by using $Ext$ functors.