Motivic Hilbert zeta functions of curves are rational

Abstract

The motivic Hilbert zeta function of a variety is the generating function for classes in the Grothendieck ring of varieties of Hilbert schemes of points of the variety. In this paper, the motivic Hilbert zeta function of a reduced curve is shown to be rational.

16 pages, 2 figures. v2: Minor changes. Final version to appear in the Journal of the Institute of Mathematics of Jussieu

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