CR singular immersions of complex projective spaces
Adam Coffman
article abstract
Quadratically parametrized smooth maps from one complex projective
space to another are constructed as projections of the Segre map of
the complexification. A classification theorem relates equivalence
classes of projections to congruence classes of matrix pencils. Maps
from the 2-sphere to the complex projective plane, which generalize
stereographic projection, and immersions of the complex projective
plane in four and five complex dimensions, are considered in detail.
Of particular interest are the CR singular points in the image.
addendum:
Some of the calculations omitted from the article appear in an
unpublished addendum.