부산대학교 도서관

In this paper, all the rings are assumed to be commutative and Noetherian. Let $A$ be a local ring such that $A\simeq R/I$ where $(R, \germ n)$ is an $n$-dimensional complete regular local ring containing a 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 in an upper triangular matrix that is called the Lyubeznik table. The authors study the Lyubeznik numbers of two homogeneous ideals of the standard graded polynomial ring $R=K[x_1, \dots, x_n]$ whose initial ideals are linked for some monomial order over $R$. Some relations between Lyubeznik and Betti numbers of homogeneous ideals are also investigated.