Some algebras with the weak Lefschetz property

David Cook, Uwe Nagel

Research output: Contribution to journalArticlepeer-review


Using a connection to lozenge tilings of triangular regions, we establish an easily checkable criterion that guarantees the weak Lefschetz property of a quotient by a monomial ideal in three variables. It is also shown that each such ideal also has a semistable syzygy bundle.

Original languageEnglish
Pages (from-to)69-80
Number of pages12
JournalSpringer INdAM Series
StatePublished - 2017

Bibliographical note

Funding Information:
Fig. 6 The region corresponding to d1 D d2 D d3 D 12 and d4 D ∆∆∆ D d8 D 11 in Example 3 Acknowledgements The second author was partially supported by the National Security Agency under Grant Number H98230-12-1-0247 and by the Simons Foundation under grants #208869 and #317096. The authors are grateful to the referee for comments that helped to improve the exposition.

Publisher Copyright:
© 2017, Springer International Publishing AG.


  • Determinants
  • Lozenge tiling
  • Monomial ideal
  • Perfect matching
  • Semistable syzygy bundle
  • Weak Lefschetz property

ASJC Scopus subject areas

  • Mathematics (all)


Dive into the research topics of 'Some algebras with the weak Lefschetz property'. Together they form a unique fingerprint.

Cite this