Geometriae Dedicata

, Volume 116, Issue 1, pp 157–202

Smooth Projective Planes

Article

DOI: 10.1007/s10711-005-9012-5

Cite this article as:
Mckay, B. Geom Dedicata (2005) 116: 157. doi:10.1007/s10711-005-9012-5
  • 50 Downloads

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.

Keywords

smooth projective plane pseudoholomorphic curve 

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.University College CorkCorkIreland

Personalised recommendations