Seminar
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| Location: | SLMath: Eisenbud Auditorium, Front Courtyard |
Lefschetz properties for artinian Gorenstein algebras
The cohomology ring of a smooth projective complex variety has the strong Lefschetz property, i.e., the multiplication maps given by powers of a general linear forms all have maximal rank. For other artinian Gorenstein algebras (commutative algebras with Poincaré duality) it is well known that this needs not be true, not even for multiplication by linear forms, which would be the weak Lefschetz property. However, there are lots of results and some conjectures about when we have the strong or the weak Lefschetz property. I will explain why I find the problems in this area interesting, and I will highlight some of the main results. At the end I will report on some recent results obtained in joint work with Juan Migliore, Rosa Maria Miró-Roig and Uwe Nagel.
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