Timeline for Is P^2 important in Kontsevich's recursion formula?
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7 events
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| May 24, 2012 at 16:31 | history | edited | Karl Schwede |
Fixed a tag
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| Mar 27, 2012 at 13:05 | comment | added | Jonny Evans | See also Aleksey Zinger's early work for a symplectic approach for the relationship between GW and enumerative invariants. I think Eleny Ionel also has an early paper on this in genus 1 for $CP^2$. | |
| Mar 27, 2012 at 12:18 | comment | added | Jason Starr | To answer Dan Petersen's question (not Ritwik's), there has been much work proving genus 0 GW invariants are enumerative, e.g., for a Fano hypersurface or Fano complete intersection which is sufficiently general in moduli, in about 2/3rds of the cases. This is work of Beheshti-Kumar (building on earlier work of Harris-Roth-Starr and Coskun-Starr). | |
| Mar 27, 2012 at 10:23 | vote | accept | Ritwik | ||
| Mar 27, 2012 at 8:57 | comment | added | Dan Petersen | The whole Gromov-Witten formalism works in quite great generality. The more delicate issue is whether the Gromov-Witten invariants have any enumerative significance. For $\mathbf P^2$ they certainly count curves, but it's not obvious: one uses that since the target space is convex, there is an honest-to-god fundamental class, and moreover one can use the action of $\mathrm{PGL}_3$ on $\mathbf P^2$ and Kleiman's transversality theorem to guarantee that intersections are sufficiently generic. I don't know off hand under how general conditions it is known that GW invariants actually count curves. | |
| Mar 27, 2012 at 7:42 | answer | added | Jonny Evans | timeline score: 11 | |
| Mar 27, 2012 at 6:59 | history | asked | Ritwik | CC BY-SA 3.0 |