부산대학교 도서관

In this paper, all the rings are assumed to be commutative andNoetherian. Let $A$ be a local ring such that $A\simeq R/I$ where $(R,\germ n)$ is an $n$-dimensional complete regular local ring containinga field $K$. The Lyubeznik numbers were defined by Lyubeznik in 1993 as$$\lambda_{i, j}(A)=\mu_i(\germ n, H^{n-j}_{I}(R))$$for $i, j\geq 0$. We know that the nonzero Lyubeznik numbers are put inan upper triangular matrix that is called the Lyubeznik table. Theauthors study the Lyubeznik numbers of two homogeneous ideals of thestandard graded polynomial ring $R=K[x_1, \dots, x_n]$ whose initialideals are linked for some monomial order over $R$. Some relationsbetween Lyubeznik and Betti numbers of homogeneous ideals are alsoinvestigated.