Monomial ideals, almost complete intersections and the Weak Lefschetz property

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...

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Veröffentlicht in:	Transactions of the American Mathematical Society 2011-01, Vol.363 (1), p.229-257
Hauptverfasser:	Migliore, Juan C., Miró-Roig, Rosa M., Nagel, Uwe
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Arithmetical algebraic geometry Combinatorics Determinants Exact sciences and technology General mathematics General, history and biography Geometria algebraica aritmètica Integers Mathematical functions Mathematical theorems Mathematics Numbers Polynomials Property titles Research article Sciences and techniques of general use Vector algebra Àlgebra Àlgebra vectorial
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Beschreibung
Zusammenfassung:	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.
ISSN:	0002-9947 1088-6850
DOI:	10.1090/S0002-9947-2010-05127-X