PreprintCC BY-SA 4.0arXiv
Matrix factorization of quotient singularities of type A and D
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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BibTeX
@misc{sharland2026matrix,
title = {{Matrix factorization of quotient singularities of type A and D}},
author = {Ayse Sharland and Meral Tosun},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28824},
eprint = {2609.28824},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28824},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Matrix factorization of quotient singularities of type A and D
AU - Ayse Sharland
AU - Meral Tosun
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28824
UR - https://arxiv.org/abs/2609.28824
AB - 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.
ER -