Mathematical Proceedings of the Cambridge Philosophical Society

On the highest Lyubeznik number

a1 Department of Mathematics, Nara University of Education, Takabatake-cho, Nara, 630-8528, Japan. e-mail:


In this paper, we will prove that the highest Lyubeznik number λd,d(A) is one if A is a Cohen–Macaualy local ring containing a field, where d is the dimension of A.

(Received March 20 2000)
(Revised September 27 2000)