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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Monomial ideals, almost complete intersections and the Weak Lefschetz property


Authors: Juan C. Migliore, Rosa M. Miró-Roig and Uwe Nagel
Journal: Trans. Amer. Math. Soc. 363 (2011), 229-257
MSC (2010): Primary 13D40, 13E10, 13C13; Secondary 13C40, 13D02, 14J60
Published electronically: August 17, 2010
MathSciNet review: 2719680
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Abstract: Many algebras are expected to have the Weak Lefschetz property, although this is often very difficult to establish. We illustrate the subtlety of the problem by studying monomial and some closely related ideals. Our results exemplify the intriguing dependence of the property on the characteristic of the ground field and on arithmetic properties of the exponent vectors of the monomials.


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Additional Information

Juan C. Migliore
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: migliore.1@nd.edu

Rosa M. Miró-Roig
Affiliation: Facultat de Matemàtiques, Department d’Algebra i Geometria, University of Barce- lona, Gran Via des les Corts Catalanes 585, 08007 Barcelona, Spain
Email: miro@ub.edu

Uwe Nagel
Affiliation: Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, Kentucky 40506-0027
Email: uwenagel@ms.uky.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05127-X
PII: S 0002-9947(2010)05127-X
Received by editor(s): January 13, 2009
Published electronically: August 17, 2010
Additional Notes: Part of the work for this paper was done while the first author was sponsored by the National Security Agency under Grant Number H98230-07-1-0036.
Part of the work for this paper was done while the second author was partially supported by MTM2007-61104.
Part of the work for this paper was done while the third author was sponsored by the National Security Agency under Grant Number H98230-07-1-0065. The authors thank Fabrizio Zanello for useful and enjoyable conversations related to some of this material. They also thank David Cook II for useful comments.
Article copyright: © Copyright 2010 American Mathematical Society