Timeline for Pull-back of an irreducible ample divisor via an isogeny of abelian varieties
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 15, 2017 at 10:06 | comment | added | Francesco Polizzi | @abx: thank you for the counterexample. I was thinking about something similar involving a $(1, \, 2)$-polarization, but your construction is simpler. | |
| Jun 15, 2017 at 9:42 | comment | added | abx | Yes, I agree... | |
| Jun 15, 2017 at 7:46 | comment | added | Francesco Polizzi | If $D$ is normal, the same is true for every finite, étale cover of $D$. In particular, the divisor $f^*D$ cannot have singularities in codimension $1$, hence $D_i \cdot D_j=0$ for $i \neq j$ and the proof given in the book should work. | |
| Jun 15, 2017 at 7:43 | vote | accept | Francesco Polizzi | ||
| Jun 14, 2017 at 19:40 | comment | added | rita | For abelian varieties of any dimension, I think $f^*D$ will be irreducible if $D$ is normal. In fact I think all counterexamples to irreducibility are similar to the one you give, and so are singular in codimension 1. | |
| Jun 14, 2017 at 16:06 | history | answered | abx | CC BY-SA 3.0 |