Orbit closures and rank schemes
Orbit closures and rank schemes
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轨道闭合和等级方案
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发表时间：
2013
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通讯作者：
G. Zwara
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作者：
Christine Riedtmann;G. Zwara
设A是代数闭域k上的有限生成结合代数，考虑k_d上A-模结构的变种A_k/.如果A是有限表示类型，则定义闭包x Om的方程对于M2 mod A K/是已知的；它们是由与M相关的适当矩阵上的秩条件给出的。我们研究了任意模的这种秩条件所定义的方案CM，并将它们与为表示箭图而定义的类似方案进行了比较，得到了关于奇点的结果。我们的一个主要定理是对A型箭图的表示M的xOM理想的刻画，这是Lakshmibai和Magyar在[12]中为A型箭图的等向箭图建立的结果。《数学学科分类(2010)》。小学14L30；中学14B05、16G20、16G70。
Let A be a finitely generated associative algebra over an algebraically closed field k, and consider the variety mod A.k/ of A-module structures on k d . In case A is of finite representation type, equations defining the closure x OM are known for M 2 mod A.k/; they are given by rank conditions on suitable matrices associated with M . We study the schemes CM defined by such rank conditions for modules over arbitraryA, comparing them with similar schemes defined for representations of quivers and obtaining results on singularities. One of our main theorems is a description of the ideal of x OM for a representation M of a quiver of type An, a result Lakshmibai and Magyar established for the equioriented quiver of type An in [12]. Mathematics Subject Classification (2010). Primary 14L30; Secondary 14B05, 16G20, 16G70.