发表机构
University of Rhode Island; Galatasaray University; The University of Tokyo（罗德岛大学; 加拉塔萨雷大学; 东京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文扩展ADE奇点与极大库恩-麦考利模的关系至A型和D型商奇点，通过投影超曲面构造显式矩阵分解和模族，并恢复所有特殊库恩-麦考利模。
AI 中文摘要
本文扩展了ADE奇点与其极大库恩-麦考利模之间的经典关系，将其推广至A型和D型商奇点。我们识别了投影超曲面，这些超曲面使我们能够构造显式的矩阵分解，并由此得到极大库恩-麦考利模族。这些超曲面还通过Oka方法给出了相应商奇点的对偶分解图。最后，我们证明了原始商奇点上的所有特殊库恩-麦考利模都可以从投影超曲面上的模中恢复出来。
英文摘要
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.
