Timeline for Criterion for transverse boundary intersection of one-parameter family in $\overline M_{g,n}(X,\beta)$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 15, 2015 at 11:14 | answer | added | JoS | timeline score: 1 | |
| May 11, 2015 at 12:43 | comment | added | JoS | Thank you very much for your help. If you find a reference please give it as an answer, so I can accept it. | |
| May 11, 2015 at 12:27 | comment | added | Jason Starr | I will try to find you a reference. Personally, I would handle it in two steps. First, the induced (1-)morphism from $B$ to the Artin stack $\mathfrak{M}_{0,n}$ of all $n$-pointed, at-worst-nodal curves pulls back the boundary divisor $\Delta$ to be $\underline{0}$, with multiplicity $1$. Second, because of convexity, the $1$-morphism $\overline{M}_{g,n}(X,\beta)\to \mathfrak{M}_{0,n}$ is smooth, so that the pullback of $\Delta$ is a Cartier divisor -- the usual boundary divisor. | |
| May 11, 2015 at 10:28 | comment | added | JoS | Ah, ok, but that would be sufficient for me. Do you happen to know a reference for this? | |
| May 11, 2015 at 10:22 | comment | added | Jason Starr | For $g=0$, that is sufficient. For larger $g$, it depends on what you mean by "transverse to the boundary" in cases where "the boundary" is not actually a Cartier divisor in the moduli stack. | |
| May 11, 2015 at 10:12 | history | asked | JoS | CC BY-SA 3.0 |