The weak Lefschetz property and powers of linear forms in 𝕂[𝕩,𝕪,𝕫]

Schenck, Hal; Seceleanu, Alexandra

doi:10.1090/S0002-9939-10-10288-3

The weak Lefschetz property and powers of linear forms in $\mathbb {K}[x,y,z]$
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by Hal Schenck and Alexandra Seceleanu PDF

Proc. Amer. Math. Soc. 138 (2010), 2335-2339 Request permission

Abstract:

We show that an Artinian quotient of an ideal $I \subseteq \mathbb {K}[x,y,z]$ generated by powers of linear forms has the Weak Lefschetz Property. If the syzygy bundle of $I$ 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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