Singularities of the nested Hilbert scheme of points of length 3, 4
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909874294620160 |
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| author | Choi, Doyoung |
| author_facet | Choi, Doyoung |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11055 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singularities of the nested Hilbert scheme of points of length 3, 4 Choi, Doyoung Algebraic Geometry Primary:14B05, 14C05, Secondary:14J17 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. |
| title | Singularities of the nested Hilbert scheme of points of length 3, 4 |
| topic | Algebraic Geometry Primary:14B05, 14C05, Secondary:14J17 |
| url | https://arxiv.org/abs/2501.11055 |