DMS Algebra Seminar

Speaker: Hal Schenck

Title: Lefschetz properties in algebra

Abstract: In algebraic geometry, the Lefschetz hyperplane theorem relates the geometry and cohomology of a smooth variety to that of a hyperplane section. Over the last decade, there has been much investigation of the Lefschetz property for a graded Artinian algebra \(A\) over a field \(k\). These questions are very tractable, because \(A\) is a finite dimensional vector space over \(k\), and \(A_i\) is zero in high degree. In this instance, the Lefschetz property is a question about if the multiplication map \(A_i-->A_{i+1}\) by a general linear form has full rank. This will be a survey talk about the property, mainly illustrated with examples.