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Zbl 1049.14042
Coffman, Adam
Real congruence of complex matrix pencils and complex projections of real Veronese varieties. (English)
[J] Linear Algebra Appl. 370, 41-83 (2003). ISSN 0024-3795

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.
[Eugenii I. Shustin (Tel Aviv)]

MSC 2000:: *14P05 Real algebraic sets
14B05 Singularities (algebraic geometry)
51N15 Projective analytic geometry
15A22 Matrix pencils
32V40 Real submanifolds in complex manifolds

Keywords: matrix pencil; matrix congruence; real projective space; CR singularity; real submanifolds of complex manifolds

Cited in: Zbl 1091.15033

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