On the algebraicity about the Hodge numbers of the Hilbert schemes of algebraic surfaces

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 Gö...

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Bibliographic Details
Published inProceedings of the Edinburgh Mathematical Society Vol. 65; no. 2; pp. 392 - 403
Main Authors Jin, Seokho, Jo, Sihun
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.05.2022
Subjects
Algebra
Physics
11F50
Hodge number
algebraicity
Hilbert scheme
11G16
11R04
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Summary: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.
ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091522000141