Abstract:
The variety VSP(f,k) of presentations of a homogeneous form

f as a sum of k powers of linear forms has in a number of examples very interesting structure. In the first lecture I will give an introduction and first

examples to the study of powersum varieties.

In the case of a general cubic form f in 6 variables the powersum

variety VSP(f,10) is a Hyperkahler 4-fold. In the second lecture I

shall discuss this result and how Noether Lefschetz divisors in the

moduli space of Hyperkahler 4-folds correspond to divisors of cubic

fourfolds that are not Noether Lefschetz.

The lectures report on work with Schreyer, Iliev and Voisin.

f as a sum of k powers of linear forms has in a number of examples very interesting structure. In the first lecture I will give an introduction and first

examples to the study of powersum varieties.

In the case of a general cubic form f in 6 variables the powersum

variety VSP(f,10) is a Hyperkahler 4-fold. In the second lecture I

shall discuss this result and how Noether Lefschetz divisors in the

moduli space of Hyperkahler 4-folds correspond to divisors of cubic

fourfolds that are not Noether Lefschetz.

The lectures report on work with Schreyer, Iliev and Voisin.