THE ARTINIAN COMPLETE INTERSECTION QUOTIENT AND THE STRONG LEFSCHETZ PROPERTY
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Abstract
It has been little known when an Artinian (point) quotient has the strong Lefschetz property. In this paper, we find the Artinian complete intersection quotient having the SLP. More precisely, we prove that if X is a complete intersection in P2 of type (2, 2) and Y is a finite set of points in P2 such that X ∪ Y is a basic configuration of type (2, a) with a ≥ 3 or (3, a) with a = 3, 4, 5, 6, then R/(IX + IY) has the SLP. We also show that if X is a complete intersection in P2 of type (3, 2) and Y is a finite set of points in P2 such that X ∪ Y is a basic configuration of type (3, 3) or (3, 4), then R/(IX + IY) has the SLP.
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