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On the elliptic genus of generalised Kummer varieties

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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]).

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  1. Fachbereich Mathematik und Informatik, Johannes-Gutenberg Universität Mainz, 55099, Mainz

    Marc A. Nieper-Wißkirchen

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  1. Marc A. Nieper-Wißkirchen
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Correspondence to Marc A. Nieper-Wißkirchen.

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The author was supported by the Deutsche Forschungsgemeinschaft.

Revised version: 14 November 2003

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Nieper-Wißkirchen, M. On the elliptic genus of generalised Kummer varieties. Math. Ann. 330, 201–213 (2004). https://doi.org/10.1007/s00208-004-0541-2

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