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.