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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:
 14P05 Real algebraic sets 14B05 Singularities (algebraic geometry) 51N15 Projective analytic geometry 15A22 Matrix pencils 32V40 Real submanifolds in complex manifolds
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##### References:
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