COSAM » Events » 2022 » April » DMS Algebra Seminar

 DMS Algebra Seminar Time: Apr 05, 2022 (02:30 PM) Location: 358 Parker Hall Details: 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.

Last updated: 04/04/2022