收缩理想与有理正态曲线的Groebner扇
Contracted ideals and the Groebner fan of the rational normal curve
摘要：
该文件有两个目标：研究了$K[x,y]$中收缩齐次理想的伴随分次环和${\bf P}^d$中有理正态曲线的理想$P$的Groebner扇。令人惊讶的是，这两个问题紧密相关。本文利用由Zebrski分解产生的数值不变量，对Cohen-Macaulay关联分次环的收缩理想进行了完全分类.我们明确地确定所有的初始理想（单项式或不）的$P$是科恩-麦考利。
英文摘要：
The paper has two goals: the study the associated graded ring of contracted homogeneous ideals in $K[x,y]$ and the study of the Groebner fan of the ideal $P$ of the rational normal curve in ${\bf P}^d$. These two problems are, quite surprisingly, very tightly related. We completely classify the contracted ideals with a Cohen-Macaulay associated graded rings in terms of the numerical invariants arising from Zariski's factorization. We determine explicitly all the initial ideals (monomial or not) of $P$ that are Cohen-Macaulay.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
