Dual elliptic structures on CP2

Details Dual elliptic structures on CP2 Dual elliptic structures on CP2

2000-08-31

arxiv.org/abs/math/0008234v2

Mathematics

Symplectic Geometry

18 pages The only difference with the first version is the mention of the thesis of Benjamin MacKay ("Duality and integrable s

Scientific paper

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 Pl\"ucker formulas, which restricts their possible sets of singularities.

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