Geometriae Dedicata

, Volume 116, Issue 1, pp 157-202

Smooth Projective Planes

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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.


smooth projective plane pseudoholomorphic curve