单项曲线上的分次完整D-模
Graded Holonomic D-modules on Monomial Curves
摘要：
本文研究了$D$ -模的完整性，当$D$是$A = k[Γ]$上的$k$ -线性微分算子的环时，$D$ -模是复数$k = \mathbb C$上仿射单项曲线的坐标环.特别地，我们考虑分次的情况下，简单的分次$D$ -模的分类和计算它们的扩张。作为一种特殊情况，给出了第一Weyl代数$D = A_1(k)$的分类.
英文摘要：
In this paper, we study the holonomic $D$-modules when $D$ is the ring of $k$-linear differential operators on $A = k[Γ]$, the coordinate ring of an affine monomial curve over the complex numbers $k = \mathbb C$. In particular, we consider the graded case, and classify the simple graded $D$-modules and compute their extensions. The classification over the first Weyl algebra $D = A_1(k)$ is obtained as a special case.
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