The asymptotic profile of χ_y-genera of Hilbert schemes of points on K3 surfaces

2014/11/04 by Jan Manschot, Manschot, Jan, Jose Miguel Zapata Rolon +1
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Number Theory (math.NT) #hep-th #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.1411.1093

16 pages, comments welcome, some typos fixed, accepted for publication in "Communication in Number theory and Physics"

arxiv created 2015/06/05 · arxiv updated 2015/06/08

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 χ_y(K3^[n]) genera of Hilbert schemes of n points on K3 surfaces. We determine asymptotic values of the coefficients of the χ_y-genus for n→ ∞ as well as their asymptotic profile.

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