Timeline for Naive question on the Jacobian of a curve
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 25, 2021 at 11:47 | vote | accept | Jana | ||
| Dec 9, 2021 at 3:14 | comment | added | Kapil | There may be more than one curve, but there are only finitely many as proved by Narasimhan and Nori. | |
| Aug 6, 2018 at 22:20 | comment | added | Xarles | @Jana In general it is difficult to compute the number of ppal polarizations on an ab. variety. Generically, if it has one, it is the only one. But also, for any $N$ there exists $N$ genus 2 curves non isomorphic with all jacobians isomorphic. | |
| Aug 6, 2018 at 20:40 | comment | added | Jana | @abx: Is there any condition under which an abelian variety has an unique principal polarization? | |
| Aug 6, 2018 at 19:50 | comment | added | abx | Yes, that is exactly what the answer says. To take another example, it is well-known that the Jacobian $J$ of the Klein quartic is isomorphic to $E^3$, where $E$ is the elliptic curve with complex multiplication by $i$; thus $J$ admits another principal polarization, which is reducible. | |
| Aug 6, 2018 at 19:37 | comment | added | Jana | @agniesky: Are you saying that the Jacobian of a fixed curve can have more than one principal polarization? That is my question. | |
| Aug 6, 2018 at 19:32 | history | answered | meh | CC BY-SA 4.0 |