Quadratic points on double planes
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911247496118272 |
|---|---|
| author | Chen, Nathan Church, Ben Pasten, Hector Vogt, Isabel |
| author_facet | Chen, Nathan Church, Ben Pasten, Hector Vogt, Isabel |
| contents | Zariski dense collections of quadratic points on curves $X$ are well-understood by results of Harris--Silverman and Vojta, but when $\dim X \geq 2$ there is not an analogous geometric characterization, even conjecturally. In this note we consider the case of a double cover $π\colon X \to \mathbb{P}^r$, where Hilbert's Irreducibility Theorem implies that the quadratic points in the fibers of $π$ are dense. We show that Vojta's Conjecture implies that, once the canonical bundle of $X$ is sufficiently positive, there are no other sources of Zariski dense quadratic points. This is complemented by several examples of surfaces $X \to \mathbb{P}^2$ with an additional source of dense quadratic points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01669 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quadratic points on double planes Chen, Nathan Church, Ben Pasten, Hector Vogt, Isabel Number Theory Algebraic Geometry 11G35 Zariski dense collections of quadratic points on curves $X$ are well-understood by results of Harris--Silverman and Vojta, but when $\dim X \geq 2$ there is not an analogous geometric characterization, even conjecturally. In this note we consider the case of a double cover $π\colon X \to \mathbb{P}^r$, where Hilbert's Irreducibility Theorem implies that the quadratic points in the fibers of $π$ are dense. We show that Vojta's Conjecture implies that, once the canonical bundle of $X$ is sufficiently positive, there are no other sources of Zariski dense quadratic points. This is complemented by several examples of surfaces $X \to \mathbb{P}^2$ with an additional source of dense quadratic points. |
| title | Quadratic points on double planes |
| topic | Number Theory Algebraic Geometry 11G35 |
| url | https://arxiv.org/abs/2511.01669 |