An Artinian Quotient of the Coordinate Ring of a Complete Intersection in ℙ n Having the Weak Lefschetz Property

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 [39].