The weak Lefschetz property and powers of linear forms in

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 | References | Similar Articles | Additional Information

Abstract: We show that an Artinian quotient of an ideal generated by powers of linear forms has the Weak Lefschetz Property. If the syzygy bundle of 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

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.