Communications in Number Theory and Physics

Volume 9 (2015)

Number 2

The asymptotic profile of $\chi_y$-genera of Hilbert schemes of points on K3 surfaces

Pages: 413 – 435

DOI: http://dx.doi.org/10.4310/CNTP.2015.v9.n2.a6

Authors

Jan Manschot (School of Mathematics, Trinity College, College Green, Dublin, Ireland)

Jose Miguel Zapata Rolon (Mathematical Institute, University of Cologne, Germany)

Abstract

The Hodge numbers of the Hilbert schemes of points on algebraic surfaces are given by Göttsche’s formula, which expresses the generating functions of the Hodge numbers in terms of theta and eta functions. We specialize in this paper to generating functions of the $\chi_y$-genera of Hilbert schemes of $n$ points on K3 surfaces. We determine asymptotic values of the coefficients of the $\chi_y$-genus for $n \to \infty$ as well as their asymptotic profile.

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Published 12 June 2015