Timeline for Evaluation maps for moduli of stable maps
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 1, 2015 at 12:08 | vote | accept | CommunityBot | ||
| Mar 24, 2015 at 17:37 | history | edited | JoS | CC BY-SA 3.0 |
Expanded by a proof of the desired property of ev when restricted to an open set of the target
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| Mar 24, 2015 at 17:21 | comment | added | JoS | So I think that surjectivity is not enough: if you look at the case $n=2, d=1, N=2$ then $ev$ is surjective as through any two points $p,q$ in $\mathbb{P}^2$ there is a line. If $(p,q)$ is not in the diagonal, there is exactly one such line, so the fibre of $ev$ is a point, for $p=q$ however the fibre is positive-dimensional (elements are in correspondence with lines through $p=q$). Hence $ev$ is not flat as fibre dimension jumps. However, I think that over a dense open subset of the target, $ev$ has the desired property. I will try to edit my answer accordingly. | |
| Mar 24, 2015 at 15:44 | comment | added | user58604 | Thanks al lot. From your argument it seems that if $ev:=ev_1\times ...\times ev_n$ is surjective then the push-forward of the structure sheaf is the structure sheaf. Am I rigth? | |
| Mar 24, 2015 at 12:33 | review | First posts | |||
| Mar 24, 2015 at 12:36 | |||||
| Mar 24, 2015 at 12:28 | history | answered | JoS | CC BY-SA 3.0 |