ON THE ALGEBRAICITY ABOUT THE HODGE NUMBERS OF THE HILBERT SCHEMES OF ALGEBRAIC SURFACES

초록

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 Gottsche'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 z1 and z2. Our result gives a refinement of the algebraicity on Betti numbers.

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