Coleff-Herrera电流、对偶和Noether算子
Coleff-Herrera currents, duality, and Noetherian operators
摘要：
设$\I$是局部自由层$\Ok(E_0)$的凝聚子层，并假定$\F=\Ok(E_0)/\I$有纯余维.从$\F$的局部自由分解得到的剩余电流$R$开始，我们构造了一个向量值Coleff-Herrera电流$μ$，其支持与$\F$相关的各种，使得$ϕ$在$\I$中当且仅当$μϕ=0$。这样一个电流$μ$也可以推导出代数Roos的基本定理的双对偶函子，这两种方法之间的关系进行了讨论。通过比约克的构造，人们可以从当前的$μ$得到$\I$的诺特算子。当前的$R$还提供了Dickenstein-Sessa分解和其他相关规范同构的显式实现。
英文摘要：
Let $\I$ be a coherent subsheaf of a locally free sheaf $\Ok(E_0)$ and suppose that $\F=\Ok(E_0)/\I$ has pure codimension. Starting with a residue current $R$ obtained from a locally free resolution of $\F$ we construct a vector-valued Coleff-Herrera current $μ$ with support on the variety associated to $\F$ such that $ϕ$ is in $\I$ if and only if $μϕ=0$. Such a current $μ$ can also be derived algebraically from a fundamental theorem of Roos about the bidualizing functor, and the relation between these two approaches is discussed. By a construction due to Björk one gets Noetherian operators for $\I$ from the current $μ$. The current $R$ also provides an explicit realization of the Dickenstein-Sessa decomposition and other related canonical isomorphisms.
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