Symmetric products and puncturing Campana-special varieties
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914198681812992 |
|---|---|
| author | Bartsch, Finn Javanpeykar, Ariyan Levin, Aaron |
| author_facet | Bartsch, Finn Javanpeykar, Ariyan Levin, Aaron |
| contents | We give a counterexample to the Arithmetic Puncturing Conjecture and Geometric Puncturing Conjecture of Hassett-Tschinkel using symmetric powers of uniruled surfaces, and propose a corrected conjecture inspired by Campana's conjectures on special varieties. We confirm Campana's conjecture on potential density for symmetric powers of products of curves. As a by-product, we obtain an example of a surface without a potentially dense set of rational points, but for which some symmetric power does have a dense set of rational points, and even satisfies Corvaja-Zannier's version of the Hilbert property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14931 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetric products and puncturing Campana-special varieties Bartsch, Finn Javanpeykar, Ariyan Levin, Aaron Algebraic Geometry We give a counterexample to the Arithmetic Puncturing Conjecture and Geometric Puncturing Conjecture of Hassett-Tschinkel using symmetric powers of uniruled surfaces, and propose a corrected conjecture inspired by Campana's conjectures on special varieties. We confirm Campana's conjecture on potential density for symmetric powers of products of curves. As a by-product, we obtain an example of a surface without a potentially dense set of rational points, but for which some symmetric power does have a dense set of rational points, and even satisfies Corvaja-Zannier's version of the Hilbert property. |
| title | Symmetric products and puncturing Campana-special varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2412.14931 |