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Real equivalence of complex matrix pencils and complex projections of real Segre varieties. (English) Zbl 1173.15003
The author constructs quadratically parametrized maps from a product of real projective spaces to a complex projective space as the composition of the Segre embedding with a projection. Further, 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. The paper contains useful descriptions of the real and complex projective spaces.
15A22Matrix pencils
14E05Rational and birational maps
14J26Rational and ruled surfaces
14P05Real algebraic sets
32V40Real submanifolds in complex manifolds
51N15Projective analytic geometry