Timeline for Is there an algorithm to compute the intersection of tautological classes on the moduli space of genus one curves?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Oct 4, 2015 at 4:55 | comment | added | Ritwik | @Tehrani: Let me elaborate a bit more; in his second comment Will Sawin indicates that there is some section of L^{12} that vanishes only on the boundary. I actually want to see what that section is (sort of in the same spirit as what Ionel does in her paper). | |
| Oct 4, 2015 at 4:49 | comment | added | Ritwik | @Tehrani: Could you elaborate a bit more on this comment? Where can I find this software and instructions on how to use it? Ideally, I would like to compute these numbers and understand what is going on. For example, the comment Will Sawin made; that $12$ looks like the number of singular cubics. I would like to know the reason behind that. I can share my email address, if you want to explain something in greater detail (for some reason exchanging too many comments is discouraged on mathoveflow). | |
| Oct 3, 2015 at 4:03 | comment | added | Mohammad Farajzadeh-Tehrani | If only calculation of specific numbers are concerned, you can use GROWI software to calculate any GW of projective space. | |
| Sep 13, 2015 at 10:38 | comment | added | Ritwik | @Dan: Thanks; I will look at that paper. | |
| Sep 12, 2015 at 8:26 | comment | added | Dan Petersen | After some googling, you could look at the paper of Graber-Kock-Pandharipande. | |
| Sep 12, 2015 at 8:10 | comment | added | Dan Petersen | On a related note, the space $\overline M_{1,1}(\mathbf P^2,d)$ is singular with boundary components of excess dimension. So you should either make sure to talk of the virtual class, or (which is possible in your case) look instead at the reduced elliptic Gromov--Witten invariants, which are obtained by integrating over the closure of the space of smooth curves. The reduced and nonreduced elliptic GW invariants aren't equal but they contain the same information. | |
| Sep 12, 2015 at 8:07 | comment | added | Dan Petersen | The intersection numbers you're asking about are the elliptic GW invariants of $\mathbf P^2$ with gravitational descendents. These are for sure known for a long time. I am not sure what is the right reference but you could start by looking through papers of Zinger. | |
| Sep 11, 2015 at 22:01 | comment | added | Ritwik | @Will: I see, I didn't know this. Hopefully someone will give a reference for this; this is precisely what I was looking for, an explicit section of the line bundle (rather a power of the line bundle). | |
| Sep 11, 2015 at 21:58 | comment | added | Will Sawin | Yes, because (I think) there is a section of the $12$th inverse power of the bundle that vanishes only on the boundary, so there should be only boundary terms. | |
| Sep 11, 2015 at 21:53 | comment | added | Ritwik | @Will: But there should also be terms of the form $\alpha_1 \mathcal{H} + \alpha_2 a + $ the term you are saying (boundary terms). Is there any reason $\alpha_1$ and $\alpha_2$ should be zero? | |
| Sep 11, 2015 at 21:50 | comment | added | Will Sawin | $L$ is pulled back from $\overline{\mathcal M}_{1,1}$ and is something like $-1/12$ times the pullback of the boundary divisor from $\overline{\mathcal M}_{1,1}$. Perhaps there is an explicit formula for this, like $\sum_{d_1=0}^d B_{d_1,d-d_1}$? | |
| Sep 11, 2015 at 21:44 | history | asked | Ritwik | CC BY-SA 3.0 |