  Let $A^{[[n]]}$ denote the $2(n - 1)$-dimensional generalised Kummer variety
constructed from the abelian surface $A$. Further, let $X$ be an arbitrary
smooth projective surface with $\int_X c_1(X)^2 \neq 0$, and $X^{[k]}$ the
Hilbert scheme of zero-dimensional subschemes of $X$ of length $k$. We give a
formula which expresses the value of any complex genus on $A^{[[n]]}$ in terms
of Chern numbers of the varieties $X^{[k]}$.
  It is shown by Ellingsrud and Stroemme how to use Bott's residue formula to
effectively calculate the Chern numbers of the Hilbert schemes $(\IP^2)^{[k]}$
of points on the projective plane. Since $\int_{\IP^2} c_1(\IP^2)^2 = 9 \neq 0$
we can use these numbers and our formula to calculate the Chern numbers of the
generalised Kummer varieties.
  A table with all Chern numbers of the generalised Kummer varieties
$A^{[[n]]}$ for $n \leq 8$ is included.
