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.
Categories: math.AG