Smooth projective planes

Details Smooth projective planes Smooth projective planes

2004-12-27

arxiv.org/abs/math/0412500v4

Geom. Dedicata 116 (2005), 157--202

Mathematics

Differential Geometry

41 pages, no figures; More minor corrections

Scientific paper

10.1007/s10711-005-9012-5

Using symplectic topology and the Radon transform, we prove that smooth 4-dimensional projective planes are diffeomorphic to $\mathbb{CP}^2$. We define the notion of a plane curve in a smooth projective plane, show that plane curves in high dimensional regular planes are lines, prove that homeomorphisms preserving plane curves are smooth collineations, and prove a variety of results analogous to the theory of classical projective planes.

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