On singular Hilbert schemes of points: Local structures and tautological sheaves

2021/01/13 by Xiaowen Hu · 1 citation
Mathematics · Computer Science · Physics and Astronomy · #math.AG #math.AC

paper · pdf · doi:10.46298/epiga.2025.12827

Abstract

We show an intrinsic version of Thomason's fixed-point theorem. Then we determine the local structure of the Hilbert scheme of at most 7 points in \mathbbA³. In particular, we show that in these cases, the points with the same extra dimension have the same singularity type. Using these results, we compute the equivariant Hilbert functions at the singularities and verify a conjecture of Zhou on the Euler characteristics of tautological sheaves on Hilbert schemes of points on ℙ³ for at most 6 points.

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• A proof of the Briançon-Iarrobino Conjecture in three dimensions

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