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摘要翻译：
本文利用簇倾斜理论的方法研究了一维超曲面奇点上的Cohen-Macaulay模及其与结合代数表示理论的关系。利用较高的几乎分裂序列和双形几何的结果，给出了簇状倾斜物体存在的一个判据，并用同调方法给出了簇状倾斜物体的完全描述。我们得到了一大类有限维对称且满足$\tau^2=\id$的2-cy倾斜代数。特别地，我们计算2-cy倾斜代数的简单和极小椭圆曲线奇点。
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英文标题：
《Cluster tilting for one-dimensional hypersurface singularities》
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作者：
Igor Burban, Osamu Iyama, Bernhard Keller, Idun Reiten
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Representation Theory 表象理论
分类描述：Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra
代数和群的线性表示，李理论，结合代数，多重线性代数
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
In this article we study Cohen-Macaulay modules over one-dimensional hypersurface singularities and the relationship with the representation theory of associative algebras using methods of cluster tilting theory. We give a criterion for existence of cluster tilting objects and their complete description by homological methods, using higher almost split sequences and results from birational geometry. We obtain a large class of 2-CY tilted algebras which are finite dimensional symmetric and satisfy $\tau^2=\id$. In particular, we compute 2-CY tilted algebras for simple and minimally elliptic curve singularities.
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PDF链接：
https://arxiv.org/pdf/0704.1249
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