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We show that an Artinian quotient of K[x, y, z] by an ideal I generated bypowers of linear forms has the Weak Lefschetz property. If the syzygy bundle ofI is semistable this follows from results of Brenner-Kaid; our proof workswithout this hypothesis, which typically does not hold.

The Weak Lefschetz Property and powers of linear forms in K[x,y,z]