Unexpected but recurrent phenomena for Quot and Hilbert schemes of points
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914843127185408 |
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| author | Giovenzana, Franco Giovenzana, Luca Graffeo, Michele Lella, Paolo |
| author_facet | Giovenzana, Franco Giovenzana, Luca Graffeo, Michele Lella, Paolo |
| contents | We investigate some aspects of the geometry of two classical generalisations of the Hilbert schemes of points. Precisely, we show that parity conjecture for $\text{Quot}_r^d\mathbb{A}^3$ already fails for $d=8$ and $r=2$ and that lots of the elementary components of the nested Hilbert schemes of points on smooth quasi-projective varieties of dimension at least 4 are generically non-reduced. We also deduce that nested Hilbert schemes of points on smooth surfaces have generically non-reduced components. Finally, we give an infinite family of elementary components of the classical Hilbert schemes of points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03146 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unexpected but recurrent phenomena for Quot and Hilbert schemes of points Giovenzana, Franco Giovenzana, Luca Graffeo, Michele Lella, Paolo Algebraic Geometry Commutative Algebra 14C05, 13D10, 13F55, 13P10 We investigate some aspects of the geometry of two classical generalisations of the Hilbert schemes of points. Precisely, we show that parity conjecture for $\text{Quot}_r^d\mathbb{A}^3$ already fails for $d=8$ and $r=2$ and that lots of the elementary components of the nested Hilbert schemes of points on smooth quasi-projective varieties of dimension at least 4 are generically non-reduced. We also deduce that nested Hilbert schemes of points on smooth surfaces have generically non-reduced components. Finally, we give an infinite family of elementary components of the classical Hilbert schemes of points. |
| title | Unexpected but recurrent phenomena for Quot and Hilbert schemes of points |
| topic | Algebraic Geometry Commutative Algebra 14C05, 13D10, 13F55, 13P10 |
| url | https://arxiv.org/abs/2403.03146 |