Titel: Powers of general linear forms and the Lefschetz properties

Abstract: It is well established that an artinian complete intersection generated by powers of general linear forms has the strong Lefschetz property. In this talk I will discuss what happens if we instead look at an almost complete intersection generated by powers of general linear forms, and for the equigenerated case, I will sketch a proof showing that this object fails even the weak Lefschetz property, except for a few special cases. The  method of proof uses Macaulay’s inverse system and a reduction to the quadratic case. No previous knowledge on the Lefschetz properties is assumed.

The talk is based on joint work with Mats Boij.