Powers of linear forms and Lefschetz properties

Understanding syzygies and other relations in polynomial rings is important in many areas of mathematics.

Powers of linear forms are in a sense the most special of all polynomials, but still ideals generated by sufficiently many powers of general linear forms seem to behave like ideals generated by general forms. This observation is the basis for the Fröberg-Iarrobino Conjectures.

In recent work together with Samuel Lundqvist, there are indications that relations between powers of smaller numbers of general linear forms may imply unexpected relations for larger numbers as well.

The aim of this project is to explore these new ideas to gain new insights in what relations are forced between powers of general linear forms in general. The most immediate consequences would be to interpolation theory.

General linear forms have also since long been essential in the field of Lefschetz Properties, which has gained much interest in the last decade with a number of remarkable breakthroughs.