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 | References | Similar Articles | Additional Information

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

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.

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© Copyright 2010
American Mathematical Society