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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The weak Lefschetz property and powers of linear forms in $ \mathbb{K}[x,y,z]$


Authors: Hal Schenck and Alexandra Seceleanu
Journal: Proc. Amer. Math. Soc. 138 (2010), 2335-2339
MSC (2010): Primary 13D02, 14J60, 13C13, 13C40, 14F05
Published electronically: February 4, 2010
MathSciNet review: 2607862
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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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Additional Information

Hal Schenck
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Email: schenck@math.uiuc.edu

Alexandra Seceleanu
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Email: asecele2@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10288-3
PII: S 0002-9939(10)10288-3
Keywords: Weak Lefschetz property, Artinian algebra, powers of linear forms
Received by editor(s): July 9, 2009
Received by editor(s) in revised form: November 6, 2009
Published electronically: February 4, 2010
Additional Notes: The first author was supported by NSF grant no. 07–07667 and NSA grant no. 904-03-1-0006
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.