Timeline for Examples of finiteness of rational points for hypersurfaces in $\mathbb P^3_{\mathbb Q}$ of degree $>4$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 26, 2012 at 14:36 | history | edited | Felipe Voloch | CC BY-SA 3.0 |
added 347 characters in body
|
| Aug 26, 2012 at 14:09 | comment | added | Jason Starr | @Felipe: The best result I know of is the result of Geng Xu cited by the OP. However, as the OP remarks, this only applies to "very general" surfaces, so potentially might fail for <I>every</I> surface defined over a number field. | |
| Aug 26, 2012 at 13:26 | comment | added | Felipe Voloch | @Jason: Good point. Can these be ruled out separately? | |
| Aug 26, 2012 at 13:11 | comment | added | Jason Starr | I'm not sure what you write is correct. Certainly a smooth rational or elliptic curve would give a divisor class on the general type hypersurface that is not commensurable with the hyperplane class. However, these surfaces may contain singular curves whose normalization has geometric genus $0$ or $1$ and whose divisor classes are multiples of the hyperplane class. | |
| Aug 26, 2012 at 13:01 | history | answered | Felipe Voloch | CC BY-SA 3.0 |