Survey article: A tour of the weak and strong Lefschetz properties

Juan Migliore, Uwe Nagel

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


An artinian graded algebra, A, is said to have the weak Lefschetz property (WLP) if multiplication by a general linear form has maximal rank in every degree. A vast quantity of work has been done studying and applying this property, touching on numerous and diverse areas of algebraic geometry, commutative algebra and combinatorics. Amazingly, though, much of this work has a "common ancestor" in a theorem originally due to Stanley, although subsequently reproved by others. In this paper we describe the different directions in which research has moved starting with this theorem, and we discuss some of the open questions that continue to motivate current research.

Original languageEnglish
Pages (from-to)329-358
Number of pages30
JournalJournal of Commutative Algebra
Issue number3
StatePublished - 2013

ASJC Scopus subject areas

  • Algebra and Number Theory


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