An equivalence linking CM-types $A_\infty$ and $D_\infty$

TL;DR

This paper establishes an equivalence between the stable categories of graded maximal Cohen-Macaulay modules over hypersurfaces of types A_infinity and D_infinity, revealing a deep connection in their algebraic structures.

Contribution

It demonstrates a specific equivalence linking the stable categories of Cohen-Macaulay modules over A_infinity and D_infinity hypersurfaces, a novel insight in algebraic geometry.

Findings

Stable categories of graded maximal Cohen-Macaulay modules are equivalent for A_infinity and D_infinity hypersurfaces.

The equivalence is established under a specific grading condition.

This links the representation theory of these two types of hypersurfaces.

Abstract

We show that, for a specific grading, the stable categories of graded maximal Cohen-Macaulay modules over hypersurfaces of type $A_\infty$ and $D_\infty$ are equivalent.