Monomial ideals, almost complete intersections and the Weak Lefschetz property

By Juan Migliore, R. Mir'o-Roig, Uwe Nagel. 2008

151 citations recorded by the source corpus.

Many algebras are expected to have the Weak Lefschetz property though 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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/68195006fdc21acddb8c8e4c7172bc4d51205761

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Uwe Nagel
2. Juan Migliore
3. R. Mir'o-Roig
4. M. Boij
5. Fabrizio Zanello
6. A. V. Geramita
7. Karim A. Adiprasito
8. Brian Harbourne

In Computational Theory and Mathematics

1. Uwe Nagel
2. Juan Migliore
3. R. Mir'o-Roig
4. M. Boij
5. Fabrizio Zanello
6. A. V. Geramita
7. Karim A. Adiprasito

In Discrete Mathematics and Combinatorics

1. Juan Migliore
2. Uwe Nagel
3. R. Mir'o-Roig
4. M. Boij
5. Fabrizio Zanello

Citations in the corpus

• On the shape of a pure O-sequence (2010, methodology): “9, [54] Example 7.”
• Survey Article: A tour of the weak and strong Lefschetz properties (2013, background): “Concerning the connection to the WLP, the following result of Migliore, Miró-Roig and Nagel gives a partial answer.”