Abstract
For a complete intersection set of points in a projective space ℙ
n
over an algebraically closed field, we prove that the h-vector of the graded Artinian ring R/(I
𝕏 + I
𝕐) is an SI-sequence provided 𝕏 is also a complete intersection subset of ℤ and 𝕐 = ℤ \ 𝕏. Furthermore, we also show that if {𝕏, 𝕐} is a regular division of a general basic configuration ℤ in ℙ
n
, then R/(I
𝕏 + I
𝕐) has the Weak Lefschetz property. These two results give positive answers to the interesting question of [Citation39].
2010 Mathematics Subject Classification:
ACKNOWLEDGMENT
The authors are truly thankful to the reviewer, whose comments and suggestions enabled us to make substantial improvements in the paper.
Notes
Communicated by I. Swanson.