Timeline for Polarizations of K3 surfaces over finite fields
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Jan 5, 2012 at 10:37 | answer | added | Remke Kloosterman | timeline score: 3 | |
| Jan 4, 2012 at 15:51 | comment | added | naf | There is indeed a notion of isogeny for K3 surfaces; see the paper of Mukai "On the moduli space of bundles on a K3 surface I" and the preprint "Fourier-Mukai partners of K3 surfaces in positive characteristic" by Lieblich and Olsson (arxiv.org/abs/1112.5114) | |
| Jan 4, 2012 at 15:38 | comment | added | naf | If $k$ is finite then $Pic(X)$ is expected to have rank at least two. It's not clear, at least to me, what to expect in this case. | |
| Jan 4, 2012 at 14:42 | comment | added | Keerthi Madapusi | Are things different for finite fields? I don't want to use the Tate conjecture. | |
| Jan 4, 2012 at 7:36 | comment | added | naf | @Keerthi: Are you assuming that $k$ is a finite field or is it just assumed to be of characteristic $>2$? | |
| Jan 3, 2012 at 21:06 | vote | accept | Keerthi Madapusi | ||
| Jan 3, 2012 at 21:06 | |||||
| Jan 3, 2012 at 20:08 | answer | added | Donu Arapura | timeline score: 10 | |
| Jan 3, 2012 at 19:48 | comment | added | Donu Arapura | I haven't thought this through carefully (my new years resolution is to limit mathoverflow activity), but suppose $k=\bar k$ and you took a general point $(X,\lambda)$ in the moduli space of polarized K3's with $\lambda^2=2p$. I suspect that you should be able to argue that $\lambda$ generates $Pic(X)$, so you would have counterexample. | |
| Jan 3, 2012 at 18:03 | history | asked | Keerthi Madapusi | CC BY-SA 3.0 |