Timeline for Quotient of an abelian surface by a finite group, irreducible components
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 3, 2010 at 14:35 | vote | accept | TonyS | ||
| Dec 3, 2010 at 12:13 | answer | added | rita | timeline score: 6 | |
| Dec 3, 2010 at 10:25 | comment | added | TonyS | Ah, interesting. Do you know some literature where i can read more about quotients of abelian varieties? PS: You can make this an answer, then i can click to set this as my accepted answer. | |
| Dec 2, 2010 at 22:21 | comment | added | rita | You are dividing an abelian variety by a finite subgroup, so the quotient is again an abelian variety (in particular $G$ acts freely on $A$ and $A/G$ is smooth). In addition in your case the group $G$ is equal to $G_1xG_2$, were $G_i$ generated by $L_i$, and the action is the product of the action of $G_i$ on $E_i$, so $A/G=E_1/G_1\times E_2/G_2$. | |
| Dec 2, 2010 at 20:52 | comment | added | TonyS | Is it really this simple? I'm not so familiar with taking qoutients. But from what i read it can be quite complicated, so for example why should $E_1/C_1$ be smooth? | |
| Dec 2, 2010 at 19:06 | comment | added | rita | If I understand correctly what you are doing, $A/G$ is just $C_1\times C_2$, where $C_i$ is the quotient of $E_i$ b the subgroup of order 2 generated by $L_i$. So it is again a product of 2 elliptic curves. | |
| Dec 2, 2010 at 18:14 | history | asked | TonyS | CC BY-SA 2.5 |