The sum of the Betti numbers of smooth Hilbert schemes
Joseph Donato, Monica Lewis, Tim Ryan, Faustas Udrenas, Zijian Zhang
TL;DR
This paper calculates the total Betti numbers for six out of seven families of smooth Hilbert schemes over projective space, providing new insights into their topological structure.
Contribution
It is the first to explicitly compute the sum of Betti numbers for most families of smooth Hilbert schemes over projective space.
Findings
Sum of Betti numbers computed for six families
Provides new topological invariants for smooth Hilbert schemes
Enhances understanding of their geometric properties
Abstract
In this paper, we compute the sum of the Betti numbers for 6 of the 7 families of smooth Hilbert schemes over projective space.
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