Maximal Cohen–Macaulay Modules Over Non–Isolated Surface Singularities and Matrix Problems

Notes on Nonisolated Singularities

This is a preliminary version of a geometric study of nonisolated singularities of functions on singular spaces. Several results are proved in this singular setting, such as obstructions to integer (co)homology groups via monodromies of nearby sections and a better control over the attaching of thimbles. This is meant to be a piece of an ampler project in progress, run jointly with Dirk Siersma...

Big Indecomposable Mixed Modules over Hypersurface Singularities

This research began as an effort to determine exactly which one-dimensional local rings have indecomposable finitely generated modules of arbitrarily large constant rank. The approach, which uses a new construction of indecomposable modules via the bimodule structure on certain Ext groups, turned out to be effective mainly for hypersurface singularities. The argument was eventually replaced by ...

Solvable Groups, Free Divisors and Nonisolated Matrix Singularities Ii: Vanishing Topology

In this paper we use the results from the first part to compute the vanishing topology for matrix singularities based on certain spaces of matrices. We place the variety of singular matrices in a geometric configuration of free divisors which are the “exceptional orbit varieties”for repesentations of solvable groups. Because there are towers of representations for towers of solvable groups, the...

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