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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.

14P05 Real algebraic sets
14B05 Singularities in algebraic geometry
51N15 Projective analytic geometry
15A22 Matrix pencils
32V40 Real submanifolds in complex manifolds
Full Text: DOI
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