Degenerations of generalized Kummer varieties

Let A be an abelian surface. The summation of n points on A induces a map from the n-th
Hilbert scheme Hilbn(A), to A. The (n − 1)-th generalized Kummer variety is by definition
the fiber of this map over the identity point of A. It is a smooth projective variety of dimension
2(n − 1), and forms one of the fundamental types of Hyperkähler varieties. In this talk, I
will present a method for constructing explicit degenerations of generalized Kummer varieties,
for any n, when the underlying abelian surface admits a type 2 Kulikov degeneration. I will
moreover discuss some features of these degenerations. This is joint work in progress with K.
Hulek and Z. Zhang.