Components of the nested Hilbert scheme of few points
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917219583131648 |
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| author | Graffeo, Michele Lella, Paolo |
| author_facet | Graffeo, Michele Lella, Paolo |
| contents | We study the existence and the schematic structure of elementary components of the nested Hilbert scheme on a smooth quasi-projective variety. Precisely, we find a new lower bound for the existence of non-smoothable nestings of fat points on a smooth $n$-fold, for $n\geqslant 4$. Moreover, we implement a systematic method to build generically non-reduced elementary components. We also investigate the problem of irreducibility of the Hilbert scheme of points on a singular hypersurface of $\mathbb A^3$. Explicitly, we show that the Hilbert scheme of points on a hypersurface of $\mathbb{A}^3$ having a singularity of multiplicity at least 5 admits elementary components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16765 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Components of the nested Hilbert scheme of few points Graffeo, Michele Lella, Paolo Algebraic Geometry Commutative Algebra 14C05, 14B05 We study the existence and the schematic structure of elementary components of the nested Hilbert scheme on a smooth quasi-projective variety. Precisely, we find a new lower bound for the existence of non-smoothable nestings of fat points on a smooth $n$-fold, for $n\geqslant 4$. Moreover, we implement a systematic method to build generically non-reduced elementary components. We also investigate the problem of irreducibility of the Hilbert scheme of points on a singular hypersurface of $\mathbb A^3$. Explicitly, we show that the Hilbert scheme of points on a hypersurface of $\mathbb{A}^3$ having a singularity of multiplicity at least 5 admits elementary components. |
| title | Components of the nested Hilbert scheme of few points |
| topic | Algebraic Geometry Commutative Algebra 14C05, 14B05 |
| url | https://arxiv.org/abs/2601.16765 |