Abstract:Hilbert schemes are an object arising from geometry and are closely related to physics and modular forms. Recently, there have been investigations from number theorists about the Betti numbers and Hodge numbers of the Hilbert schemes of points of an algebraic surface. In this paper, we prove that Göttsche's generating function of the Hodge numbers of Hilbert schemes of
$n$
points of an algebraic surface is algebraic at a CM point
$\tau$
and rational numbe… Show more
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