Timeline for Weight 3 modular form associated to singular abelian surfaces?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 9, 2020 at 1:09 | comment | added | reuns | For the intuition: for $f\in M_k(\Gamma)$ the period polynomials make $\Bbb{C}[X]_{\deg \le k-2}$ into a $\Gamma$ module, quotienting $\Bbb{C}[X]_{\deg \le k-2}$ by the action of $\Gamma$ gives a dimension $k-1$ complex torus which in general is not algebraic. If it is then it is a dimension dimension $k-1$ abelian variety. | |
| Mar 9, 2020 at 0:21 | comment | added | Benighted | @reuns Someone can probably give a better comment than me, but if a $d$-dimensional variety is modular, I think it is expected that the weight should be $d+1$. For example, elliptic curves correspond to weight 2 forms, and rigid Calabi-Yau threefolds give weight 4 forms. So K3 and abelian surfaces should be weight 3. | |
| Mar 8, 2020 at 23:19 | comment | added | reuns | May I ask why it is of weight 3 ? | |
| Mar 8, 2020 at 22:43 | comment | added | Kimball | This paper discusses modularity of products of elliptic cuvers. It refers to some examples by Howe for products of elliptic curves with CM. Maybe check there? | |
| Mar 8, 2020 at 22:30 | answer | added | Donu Arapura | timeline score: 2 | |
| Mar 8, 2020 at 22:08 | history | edited | Benighted | CC BY-SA 4.0 |
added 18 characters in body
|
| Mar 8, 2020 at 21:28 | history | asked | Benighted | CC BY-SA 4.0 |