On the relation between formal grade and depth with a view toward vanishing of Lyubeznik numbers

ABSTRACT

Let (R,𝔪) be a local ring and I an ideal. The aim of the present paper is twofold. At first we continue the investigation to compare fgrade(I,R) with depth R∕I and further we derive some results on the vanishing of Lyubeznik numbers.

KEYWORDS:

• Depth
• formal grade
• local cohomology
• Lyubeznik numbers

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• 13D45
• 14C14

Acknowledgments

The authors are grateful to Josep Àlvarez Montaner and Matteo Varbaro for careful reading of the earlier draft of this paper. Their useful comments make this paper readable. Last but not least, we would like thank the anonymous referee for his/her helpful remarks and suggestions.