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- Title
On the elliptic genus of generalised Kummer varieties.
- Authors
Marc A. Nieper-Wißkirchen
- Abstract
Borisov and Libgober ([2]) recently proved a conjecture of Dijkgraaf, Moore, Verlinde, and Verlinde (see [6]) on the elliptic genus of a Hilbert scheme of points on a surface. We show how their result can be used together with our work on complex genera of generalised Kummer varieties [17] to deduce the following formula, conjectured by Kawai and Yoshioka ([15]), on the elliptic genus of a generalised Kummer variety A [[n> ]] of dimension 2( n-1): Here is the weak Jacobi form of weight -1 and index and V( n) is the Hecke operator sending Jacobi forms of index r to Jacobi forms of index nr (see [7]).
- Subjects
KUMMER surfaces; JACOBI forms; QUARTIC surfaces; GEOMETRIC surfaces
- Publication
Mathematische Annalen, 2004, Vol 330, Issue 2, p201
- ISSN
0025-5831
- Publication type
Article