贝蒂表与 licci 性质
Betti Tables and the Licci Property
AI总结：
研究理想的 licci 性质与贝蒂表的关系，通过实例表明含变量立方的理想，其 licci 性质不能仅由贝蒂表确定；而含变量平方的理想，其 licci 性质由贝蒂表前两列完全确定。
AI中文摘要：
我们证明，一般而言，理想的 licci 性质不能仅由其贝蒂表确定。通过展示两个包含变量立方的\(\mathfrak{m}\)-主单项式理想，它们具有相同的贝蒂表，但只有一个是 licci 的。相反，对于包含每个变量平方的单项式理想，licci 性质完全由贝蒂表确定，实际上由其前两列确定。
英文摘要：
We show that the licci property of an ideal cannot, in general, be determined from its Betti table by exhibiting two $\mathfrak{m}$-primary monomial ideals containing the cubes the variables that have identical Betti tables, yet only one is licci. In contrast, we show that for monomial ideals containing the square of each variable, the licci property is completely determined by the Betti table; indeed, it is determined by its first two columns.
