论文标题
局部同胞模块之间的同构作为泰勒系列的截断
Isomorphisms Between Local Cohomology Modules As Truncations of Taylor Series
论文作者
论文摘要
让$ r $成为一个标准的分级多项式环，在一个字段中有限生成，让$ i $是$ r $的同质质量理想。 Bhatt，Blickle，Lyubeznik，Singh和Zhang检查了$ r/i^t $的本地协同组，因为$ t $是任意的。这样的环被称为$ r/i $的增稠。我们认为$ r = \ mathbb {f} [x] $，其中$ \ mathbb {f} $是特征0，$ x $的字段，$ x $是$ 2 \ times m $矩阵，而$ i $是由两个未成年人大小生成的理想。我们为$ r/i $增厚的本地同种学模块提供了混凝土构造。奇怪的是，可以使用Taylor系列的自然日志来描述这些局部的共同体学模块。
Let $R$ be a standard graded polynomial ring that is finitely generated over a field, and let $I$ be a homogenous prime ideal of $R$. Bhatt, Blickle, Lyubeznik, Singh, and Zhang examined the local cohomology of $R/I^t$, as $t$ grows arbitrarily large. Such rings are known as thickenings of $R/I$. We consider $R = \mathbb{F}[X]$ where $\mathbb{F}$ is a field of characteristic 0, $X$ is a $2 \times m$ matrix, and $I$ is the ideal generated by size two minors. We give concrete constructions for the local cohomology modules of thickenings of $R/I$. Bizarrely, these local cohomology modules can be described using the Taylor series of natural log.
