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Hilbert schemes of points and Fulton-MacPherson compactifications

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arxiv 2501.08269 v1 pith:A2KI3PIZ submitted 2025-01-14 math.AG

Denis Nesterov This is my paper · ORCID
classification math.AG
keywords hilbertschemescompactificationsfulton-macphersonpointsapplicationsconditionderive
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We relate Hilbert schemes of points and Fulton-MacPherson compactifications by an interpolating stability condition. We then derive wall-crossings formulas and some applications for the enumerative geometry of Hilbert schemes.

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  1. Torelli loci, product cycles, and the homomorphism conjecture for $\mathcal{A}_g$

    math.AG 2026-01 conditional novelty 7.0 of 10

    For 2≤g≤8, taut([J_g]·[A_2×A_{g-2}]) = taut([J_g])·taut([A_2×A_{g-2}]), and similarly for ([J_6],[A_3×A_3]); the paper also constructs new Gorenstein-kernel classes in compact-type moduli spaces.

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