A surface with representable $\text{CH}_{0}$-group but no universal zero-cycle
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912953697042432 |
|---|---|
| author | Alexandrou, Theodosis |
| author_facet | Alexandrou, Theodosis |
| contents | We introduce a new obstruction to the existence of a universal $0$-cycle on a smooth projective complex variety. As an application, we construct a smooth projective complex surface whose Chow group of $0$-cycles is representable but which does not admit a universal $0$-cycle. This provides a two-dimensional analogue of Voisin's recent threefold counterexample to a question of Colliot-Thélène. As a further consequence, we exhibit the first example of a smooth projective threefold of Kodaira dimension zero carrying a non-torsion Hodge class of degree $4$ that is not algebraic. The construction relies on the geometry of bielliptic surfaces of type 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13435 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A surface with representable $\text{CH}_{0}$-group but no universal zero-cycle Alexandrou, Theodosis Algebraic Geometry K-Theory and Homology 14C25 (Primary) 14C30, 14J27 (Secondary) We introduce a new obstruction to the existence of a universal $0$-cycle on a smooth projective complex variety. As an application, we construct a smooth projective complex surface whose Chow group of $0$-cycles is representable but which does not admit a universal $0$-cycle. This provides a two-dimensional analogue of Voisin's recent threefold counterexample to a question of Colliot-Thélène. As a further consequence, we exhibit the first example of a smooth projective threefold of Kodaira dimension zero carrying a non-torsion Hodge class of degree $4$ that is not algebraic. The construction relies on the geometry of bielliptic surfaces of type 2. |
| title | A surface with representable $\text{CH}_{0}$-group but no universal zero-cycle |
| topic | Algebraic Geometry K-Theory and Homology 14C25 (Primary) 14C30, 14J27 (Secondary) |
| url | https://arxiv.org/abs/2602.13435 |