Real equivalence of complex matrix pencils and complex projections of
real Segre varieties
article abstract
Quadratically parametrized maps from a product of real projective
spaces to a complex projective space are constructed as the
composition of the Segre embedding with a projection. A
classification theorem relates equivalence classes of projections to
equivalence classes of complex matrix pencils. One low-dimensional
case is a family of maps whose images are ruled surfaces in the
complex projective plane, some of which exhibit hyperbolic CR
singularities. Another case is a set of maps whose images in complex
projective 4-space are projections of the real Segre threefold.