On the Chern numbers of the generalised Kummer varieties
| dc.creator | Nieper-Wisskirchen, Marc Arnold | |
| dc.date | 2002-04-15 | |
| dc.date | 2002-04-26 | |
| dc.date.accessioned | 2026-07-07T04:47:43Z | |
| dc.date.available | 2026-07-07T04:47:43Z | |
| dc.description | 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. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/math/0204197 | |
| dc.identifier | http://arxiv.org/abs/math/0204197 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63828 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14C05 | |
| dc.title | On the Chern numbers of the generalised Kummer varieties | |
| dc.type | text |