Timeline for Curves with negative self intersection in the product of two curves
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 24, 2009 at 19:41 | comment | added | JSE | Sure, but as you say, if there's an example of the phenomenon you're looking for, it'll occur for highly non-generic C1 and C2. | |
| Oct 24, 2009 at 9:34 | comment | added | Dmitri Panov | The problem here is that for a generic product C1 x C2 its space H^(1,1)(Z) has dimension 2, and generated by curves C1 and C2. The effective cone is the positive octant aC1+bC2 with a>=0, b>=0. So for a generic product C1xC2 all curves inside have non-negative self intersections... | |
| Oct 24, 2009 at 5:07 | comment | added | JSE | OK, I edited mine to remove the stuff that was wrong but preserve the suggestion to ask first whether the phenomenon Dmitri asks about can happen "numerically." | |
| Oct 24, 2009 at 4:43 | comment | added | David E Speyer | By the way, I disagree that there is not point in our posts staying up. It is worthwhile to know what doesn't work. If you like, I'll edit mine to stand alone. | |
| Oct 24, 2009 at 4:37 | comment | added | David E Speyer | I have no idea whether this is in the effective cone. Do you know what the effective cone looks like here? | |
| Oct 24, 2009 at 4:30 | comment | added | JSE | Say, I can't delete my own posts! Assuming this is right there's no reason for either mine or yours to stay up. Is a sequence of cohomology classes like yours going to be in the effective cone? If so, I suppose you'd find in the classes the curves that Dmitri wants? | |
| Oct 24, 2009 at 3:50 | history | answered | David E Speyer | CC BY-SA 2.5 |