On Cohen-Macaulay modules over surface singularities

TL;DR

This paper classifies Cohen-Macaulay modules over certain surface singularities, showing that only specific types are tame while others are wild, advancing understanding of module behavior in algebraic geometry.

Contribution

It provides a detailed classification of Cohen-Macaulay modules over cusp and unimodule hypersurface singularities, identifying which are tame or wild.

Findings

Cusp and unimodule hypersurface singularities are classified regarding Cohen-Macaulay modules.

Only simple elliptic and cusp singularities are tame among minimally elliptic singularities.

All other minimally elliptic singularities and their quotients are wild.

Abstract

A description of Cohen-Macaulay modules over cusp surface singularities and over unimodule hypersurface singularities of type T is given. It is proved that among minimally elliptic singularities and their quotients only simple elliptic and cusps are tame, all others are wild (with respect to the classification of Cohen-Macaulay modules).