Mathematics – Commutative Algebra
Scientific paper
2011-09-26
Mathematics
Commutative Algebra
18 pages, 3 figures. Added three references in section 6 and in the bibliography
Scientific paper
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 expository 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.
Migliore Juan
Nagel Uwe
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