Timeline for morphisms from abelian varieties to rational curves.
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 1, 2009 at 5:13 | comment | added | Tony Pantev | Ah! I see. I misunderstood the question and thought that $\sigma$ can be any automorphism of $A$ as a variety, not as a group. | |
| Dec 1, 2009 at 4:22 | comment | added | Pete L. Clark | JSE's comment is well-taken (as is his example). Nevertheless, TP's example was the first one that leapt to my mind as well: the fact that for an (ample, basepoint free) line bundle L on an abelian variety A, the group of translations on A commuting with the corresponding morphism to projective space is the finite group Ker Phi_L: A -> A^{\vee} is of vital importance in the geometry of abelian varieties, e.g. in Mumford's definition of theta groups. | |
| Dec 1, 2009 at 3:50 | comment | added | JSE | Regarding this, Tony, there's a notational question of whether translations count for the poster as automorphisms of the abelian variety -- for me, Aut(A) consists of automorphisms of the variety preserving the identity. | |
| Dec 1, 2009 at 3:26 | history | answered | Tony Pantev | CC BY-SA 2.5 |