On the weak Lefschetz property for artinian Gorenstein algebras of codimension three

Authors

Mats Boij, Royal Institute of Technology,
Juan Migliore, University of Notre Dame
Rosa Miro-Roig, Gran Via des les Corts Catalanes
Uwe Nagel, University of Kentucky
Fabrizio Zanello, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

2-2014

Abstract

We study the problem of whether an arbitrary codimension three graded artinian Gorenstein algebra has the WeakLefschetz Property. We reduce this problem to checking whether it holds for all compressed Gorenstein algebras ofodd socle degree. In the first open case, namely Hilbertfunction (1, 3, 6, 6, 3, 1), we give a complete answer in every characteristic by translating the problem to one of studying geometric aspects of certain morphisms from P² to P³, and Hesse configurations in P².

Publisher's Statement

© 2014 Elsevier Inc. All rights reserved. Publisher’s version of record: https://doi.org/10.1016/j.jalgebra.2014.01.003

Publication Title

Journal of Algebra

Recommended Citation

Boij, M., Migliore, J., Miro-Roig, R., Nagel, U., & Zanello, F. (2014). On the weak Lefschetz property for artinian Gorenstein algebras of codimension three. Journal of Algebra, 403, 48-68. http://doi.org/10.1016/j.jalgebra.2014.01.003
Retrieved from: https://digitalcommons.mtu.edu/math-fp/53