Coleff-Herrera currents, duality, and noetherian operators
Coleff-Herrera currents, duality, and noetherian operators
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Coleff-Herrera 电流、对偶性和诺特算子
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发表时间：
2009
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通讯作者：
M. Andersson
中科院分区：
文献类型：
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作者：
M. Andersson
令 I 为局部自由束 O(E-0) 的相干子束，并假设 I = O(E-0)/I 具有纯余维数。从 I 的局部自由分辨率获得的剩余电流 R 开始，我们构造 a。向量值 Coleff-Herrera 电流它支持与 I 相关的变化，当且仅当 mu phi = 0 时 phi 才在 I 中。这样的电流 mu 也可以从 Roos 关于二元化函子的基本定理代数导出，并且讨论了这两种方法之间的关系。通过 Bjork 的构造，我们可以从当前的 mu 中得到 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。
Let I be a coherent subsheaf of a locally free sheaf O(E-0) and suppose that I = O(E-0)/I has pure codimension. Starting with a residue current R obtained from a locally free resolution of I we construct a. vector-valued Coleff-Herrera current it with support on the variety associated to I such that phi is in I if and only if mu phi = 0. Such a current mu 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 Bjork one gets Noetherian operators for I from the current mu. The current R also provides an explicit realization of the Dickenstein-Sessa decomposition and other related canonical isomorphisms.