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.