Timeline for Compactness as a consequence of the adjunction formula for genus second homology class
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 17, 2021 at 16:59 | comment | added | Luigi M | thanks a lot! everything makes much more sense now! | |
| Mar 17, 2021 at 16:58 | vote | accept | Luigi M | ||
| Mar 17, 2021 at 16:18 | comment | added | Chris Gerig | Because I’m assuming the manifold is not a blowup. Use adjunction inequality to see that $\chi(C) + 2[C]^2 \ge0$. | |
| Mar 17, 2021 at 16:17 | comment | added | Luigi M | I see, thanks a lot for the clarification Chris. but then in your answer, how do you exclude the case $[C]^2 <0$ (which I think is the reason why you can conclude that either $k=1$ or is a square zero torus) | |
| Mar 17, 2021 at 15:59 | comment | added | Chris Gerig | They can certainly be J-holomorphic (your comment about forbidding negative self-intersection is false), consider the blowup of CP2 with standard complex structure and the exceptional divisor. Anyway, multiple covers will have negative virtual dimension. | |
| Mar 17, 2021 at 15:57 | comment | added | Luigi M | Dear Chris, thanks a lot! can I ask you why exceptional spheres might cause a problem? they are not $J$-hol since by definition they have negative self-intersection, how do they arise in this context? | |
| Mar 17, 2021 at 15:08 | history | answered | Chris Gerig | CC BY-SA 4.0 |