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Smooth projective planes

Benjamin McKay
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Abstract

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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Benjamin McKay. 2004-12-27. Smooth projective planes. https://doi.org/10.1007/s10711-005-9012-5

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