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

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

2009-11-04

arxiv.org/abs/0911.0876v1

Proceedings of the A.M.S., 138 (2010) 2335-2339

Mathematics

Commutative Algebra

5 pages, to appear in PAMS

Scientific paper

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

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