Skew graded $(A_\infty)$ hypersurface singularities

TL;DR

This paper investigates the properties of a skew graded $(A_ abla)$ hypersurface singularity, revealing its infinite Cohen-Macaulay representation type and non-isolated singularity status in the noncommutative graded setting.

Contribution

It introduces a skew version of graded $(A_ abla)$ hypersurface singularities and analyzes their Cohen-Macaulay modules, showing new properties about their representation type and singularity nature.

Findings

A skew graded $(A_ abla)$ hypersurface singularity has countably infinite Cohen-Macaulay representation type.

Such singularities are not noncommutative graded isolated singularities.

The stable category of graded maximal Cohen-Macaulay modules over these singularities is studied.

Abstract

For a skew version of a graded $(A_\infty)$ hypersurface singularity $A$, we study the stable category of graded maximal Cohen-Macaulay modules over $A$. As a consequence, we see that $A$ has countably infinite Cohen-Macaulay representation type and is not a noncommutative graded isolated singularity.