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arXiv · 2501.11055

Singularities of the nested Hilbert scheme of points of length 3, 4

Doyoung Choi
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Abstract

We show that the projection morphism $X^{[3,4]} \lra X^{[3]}$ is flat even if it has reducible fiber. After analyzing blow-up constructions related to $X^{[3,4]}$, we conclude that $X^{[3,4]}$ has canonical Gorenstein singularities. As a corollary, we specify the singularities of several nested Hilbert schemes.

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Doyoung Choi. 2025-01-19. Singularities of the nested Hilbert scheme of points of length 3, 4. https://arxiv.org/abs/2501.11055

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