The paper constructs epsilon-weighted subschemes on Fulton-MacPherson degenerations that interpolate between Hilbert schemes and Fulton-MacPherson compactifications, and proves wall-crossing formulas that relate their tautological integrals.
Weighted compactifications of configuration spaces and relative stable degenerations
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abstract
We study a compactification of the configuration space of n distinct labeled points on an arbitrary nonsingular variety. Our construction provides a generalization of the original Fulton-MacPherson compactification that is parallel to the generalization of the moduli space of n-pointed stable curves carried out by Hassett.
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Hilbert schemes of points and Fulton-MacPherson compactifications
The paper constructs epsilon-weighted subschemes on Fulton-MacPherson degenerations that interpolate between Hilbert schemes and Fulton-MacPherson compactifications, and proves wall-crossing formulas that relate their tautological integrals.