The classification of special Cohen–Macaulay modules
The classification of special Cohen–Macaulay modules
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DOI：
10.1007/s00209-009-0501-3
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发表时间：
2008-09
影响因子：
0.8
通讯作者：
O. Iyama;M. Wemyss
中科院分区：
文献类型：
--
作者：
O. Iyama;M. Wemyss
在本文中，我们对所有二维商奇点的最小分辨率的对偶图中的异常曲线对应的所有特殊 Cohen-Macaulay (=CM) 模块进行了完全分类。在每种情况下，我们都会以组合方式明确展示特价商品。我们的结果依赖于实现特殊性，因为那些 CM 模块的第一个 Ext 组在环 R 上消失，从而将问题简化为 AR 箭袋上的组合问题； Auslander 和 Reiten 对这种可能的 AR 箭袋进行了分类。我们还给出了特殊 CM 模及其相应的重构代数的一些一般同调性质。
In this paper we completely classify all the special Cohen–Macaulay (=CM) modules corresponding to the exceptional curves in the dual graph of the minimal resolutions of all two dimensional quotient singularities. In every case we exhibit the specials explicitly in a combinatorial way. Our result relies on realizing the specials as those CM modules whose first Ext group vanishes against the ringR, thus reducing the problem to combinatorics on the AR quiver; such possible AR quivers were classified by Auslander and Reiten. We also give some general homological properties of the special CM modules and their corresponding reconstruction algebras.