论文标题
无平方groebner变形的连接性
Connectedness of square-free Groebner Deformations
论文作者
论文摘要
令$ i \ subseteq s = k [x_1，\ ldots，x_n] $是一个均匀的理想，配备了单一订单$ <$。我们表明，如果$ \ operatorName {in} _ <（i）$是一个无方形的单一理想，则$ s/i $和$ s/\ s/\ permatatorName {in} _ <（i）$具有相同的连接性维度。我们还表明，与这些商环的连接性有关的图具有相同数量的组件。我们还提供有关Lyubeznik数字的后果。我们通过进一步研究局部环中的连接性模量参数来获得这些结果。
Let $I\subseteq S=K[x_1,\ldots,x_n]$ be a homogeneous ideal equipped with a monomial order $<$. We show that if $\operatorname{in}_<(I)$ is a square-free monomial ideal, then $S/I$ and $S/\operatorname{in}_<(I)$ have the same connectedness dimension. We also show that graphs related to connectedness of these quotient rings have the same number of components. We also provide consequences regarding Lyubeznik numbers. We obtain these results by furthering the study of connectedness modulo a parameter in a local ring.
