Timeline for Picard groups of quartic K3 surfaces
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 5, 2016 at 8:33 | comment | added | Lazzaro Campeotti | @FrancescoPolizzi: a bit more simply, I guess one could take $F_6$ to be a sextic with $d$ tritangent lines; the double cover will then have Picard rank $1+d$. For small values of $d$ this should be easy enough to do by hand. | |
| May 5, 2016 at 6:04 | comment | added | Francesco Polizzi | It is possible to construct a K3 surface $S$ with Picard rank $2$ by taking a double cover of the plane of the form $w^2=F_6(x, \, y, \, z)$, where $F_6$ is a smooth plane sextic curve which admits a six-tangent conic. The surface $S$ does not sit naturally in $\mathbb{P}^4$, but in the weighted projective space $\mathbb{P}(1, \, 1, \, 1, \, 3)$. See Example 20 here: www-fourier.ujf-grenoble.fr/sites/ifmaquette.ujf-grenoble.fr/… | |
| May 4, 2016 at 13:24 | comment | added | user80337 | This is very helpful indeed! Thank you! Do you also know of any examples with Picard rank between 2 and 19 (inclusive)? I ask this because I'm trying to test some claims, so the more examples I can find, the easier my life will be. | |
| May 4, 2016 at 12:15 | history | answered | Francesco Polizzi | CC BY-SA 3.0 |