Unboundedness of zero-cycles on higher dimensional Fano manifolds
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909936823304192 |
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| author | Voisin, Claire |
| author_facet | Voisin, Claire |
| contents | We show that, unlike del Pezzo surfaces, higher dimensional Fano manifolds do not satisfy in general boundedness properties for their ${\rm CH}_0$ group of $0$-cycles. For example, for quartic threefolds having a point of odd degree, there is no ``Coray type" uperbound on the minimal odd degrees of points. Also, the ${\rm CH}_0$-group of Fano hypersurfaces can be ``unbounded'' (a notion which is related to infinite dimensionality in the sense of Mumford), meaning that there is no integer $N$ such that $0$-cycles of degree at least $N$ are effective. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_23080 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unboundedness of zero-cycles on higher dimensional Fano manifolds Voisin, Claire Algebraic Geometry Number Theory We show that, unlike del Pezzo surfaces, higher dimensional Fano manifolds do not satisfy in general boundedness properties for their ${\rm CH}_0$ group of $0$-cycles. For example, for quartic threefolds having a point of odd degree, there is no ``Coray type" uperbound on the minimal odd degrees of points. Also, the ${\rm CH}_0$-group of Fano hypersurfaces can be ``unbounded'' (a notion which is related to infinite dimensionality in the sense of Mumford), meaning that there is no integer $N$ such that $0$-cycles of degree at least $N$ are effective. |
| title | Unboundedness of zero-cycles on higher dimensional Fano manifolds |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2511.23080 |