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arXiv · 2609.28824

Matrix factorization of quotient singularities of type A and D

Ayse Sharland·Meral Tosun
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Abstract

In this article, we extend the classical relationship between ADE singularities and their maximal Cohen-Macaulay modules to quotient singularities of types A and D. We identify projected hypersurfaces which allow us to construct explicit matrix factorizations, and in return, families of maximal Cohen-Macaulay modules. These hypersurfaces also yield the dual resolution graphs of the corresponding quotient singularities via Oka's method. Finally, we show that all special Cohen-Macaulay modules over the original quotient singularity can be recovered from those over the projected hypersurfaces.

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Ayse Sharland, Meral Tosun. 2026-09-23. Matrix factorization of quotient singularities of type A and D. https://arxiv.org/abs/2609.28824

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