Skew graded $(A_\infty )$ hypersurface singularities

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.