光滑射影平面
Smooth projective planes
摘要：
利用辛拓扑和Radon变换，证明了光滑的四维射影平面与$\mathbb{CP}^2$是同构的.我们定义了光滑射影平面中的平面曲线的概念，证明了高维正则平面中的平面曲线是直线，证明了保持平面曲线的同胚是光滑直射，并证明了与经典射影平面理论类似的各种结果。
英文摘要：
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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