Dual elliptic structures on CP2
| dc.creator | Sikorav, Jean-Claude | |
| dc.date | 2000-08-31 | |
| dc.date | 2000-10-12 | |
| dc.date.accessioned | 2026-07-07T04:37:04Z | |
| dc.date.available | 2026-07-07T04:37:04Z | |
| dc.description | We consider an almost complex structure J on CP2, or more generally an elliptic structure E which is tamed by the standard symplectic structure. An E-curve is a surface tangent to E (this generalizes the notion of J(holomorphic)-curve), and an E-line is an E-curve of degree 1. We prove that the space of E-lines is again a CP2 with a tame elliptic structure E^*, and that each E-curve has an associated dual E^*-curve. This implies that the E-curves, and in particular the J-curves, satisfy the Plücker formulas, which restricts their possible sets of singularities. | |
| dc.description | 18 pages The only difference with the first version is the mention of the thesis of Benjamin MacKay ("Duality and integrable systems of pseudoholomorphic curves", Duke University, 1999), which I did not know at the time, and which contains a large part of the results of my paper | |
| dc.identifier | https://arxiv.org/abs/math/0008234 | |
| dc.identifier | http://arxiv.org/abs/math/0008234 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59826 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 32Q65 (Primary) 53C15, 53C42, 53D35, 57R17, 58J60 (Secondary) | |
| dc.title | Dual elliptic structures on CP2 | |
| dc.type | text |