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Zbl 1173.15003
Coffman, Adam
Real equivalence of complex matrix pencils and complex projections of real Segre varieties. (English)
[J] Electron. J. Linear Algebra 17, 651-698, electronic only (2008). ISSN 1081-3810/e

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.
[A. Arvanitoyeorgos (Patras)]

MSC 2000:: *15A22 Matrix pencils
14E05 Birational correspondences
14J26 Surfaces (rational and ruled)
14P05 Real algebraic sets
32V40 Real submanifolds in complex manifolds
51N15 Projective analytic geometry

Keywords: matrix pencil; matrix equivalence; ruled surface; Segre embedding; CR singularity; complex projective space

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