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Real congruence of complex matrix pencils and complex projections of real Veronese varieties. (English) Zbl 1049.14042
The paper treats the classification problem of homogeneous quadratic maps of a real projective space to a complex projective space via its relation to the congruence problem of pencils of symmetric matrices and the real classification of complex quadrics. The low-dimensional examples of quadratic curves in the Riemann sphere and of the models of the real projective plane in the complex four-space are considered in detail, resulting in a list of normal forms of real submanifolds of complex spaces with CR singularities.

MSC:
14P05Real algebraic sets
14B05Singularities (algebraic geometry)
51N15Projective analytic geometry
15A22Matrix pencils
32V40Real submanifolds in complex manifolds