Kieran O'Grady

Title: Compact Tori associated to hyperkähler varieties of Kummer type

Abstract: 
Let X be a hyperkähler variety of Kummer type. Then H^3(X) has dimension 8, 
and hence there is an associated 4-dimensional compact complex torus J^3(X). 
If X is projective J^3(X) is an abelian variety. I will show how to reconstruct 
explicitly J^3(X) starting from the Hodge structure on H^2(X). In particular, 
it will follow that J^3(X) is of Weil type. We expect that, by looking closely 
into J^3(X), one will find explicit locally complete families of projective 
hyperkähler varieties of Kummer type.