双滤D-模的多重度
Multidegree for bifiltered D-modules
摘要：
在交换代数中，E.米勒和B。Sturmfels定义了多重分次多项式环上多重分次模的多重度的概念。我们将这一理论应用于Weyl代数D上的双滤模。双过滤是由微分算子的阶的标准过滤和沿着由M定义的周围空间的坐标子簇的所谓V-过滤的组合。柏原我们定义的多重度为D-模提供了一个新的不变量。我们研究了它与Y.劳伦特我们从I. M. Gelfand，M. M. Kapranov和A. V·泽列文斯基。我们考虑沿原点的V-过滤。当由矩阵A定义的复曲面射影簇是Cohen-Macaulay时，我们得到了超几何系统的多重度的一个显式公式。
英文摘要：
In commutative algebra, E. Miller and B. Sturmfels defined the notion of multidegree for multigraded modules over a multigraded polynomial ring. We apply this theory to bifiltered modules over the Weyl algebra D. The bifiltration is a combination of the standard filtration by the order of differential operators and of the so-called V-filtration along a coordinate subvariety of the ambient space defined by M. Kashiwara. The multidegree we define provides a new invariant for D-modules. We investigate its relation with the L-characteristic cycles considered by Y. Laurent. We give examples from the theory of A-hypergeometric systems defined by I. M. Gelfand, M. M. Kapranov and A. V. Zelevinsky. We consider the V-filtration along the origin. When the toric projective variety defined from the matrix A is Cohen-Macaulay, we have an explicit formula for the multidegree of the hypergeometric system.
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