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On the algebraicity about the Hodge numbers of the Hilbert schemes of algebraic surfaces
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 65 / Issue 2 / May 2022
- Published online by Cambridge University Press:
- 19 April 2022, pp. 392-403
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- Article
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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 numbers $z_1$
and $z_2$
. Our result gives a refinement of the algebraicity on Betti numbers.
