Abstract
We show that an Artinian quotient of an ideal I ⊆ K [ x , y , z ] I \subseteq \mathbb {K}[x,y,z] generated by powers of linear forms has the Weak Lefschetz Property. If the syzygy bundle of I I is semistable, the property follows from results of Brenner-Kaid. Our proof works without this hypothesis, which typically does not hold.
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