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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.
MSC:
15A22Matrix pencils
14E05Rational and birational maps
14J26Rational and ruled surfaces
14P05Real algebraic sets
32V40Real submanifolds in complex manifolds
51N15Projective analytic geometry