Coffman, Adam Real equivalence of complex matrix pencils and complex projections of real Segre varieties. (English) Zbl 1173.15003 Electron. J. Linear Algebra 17, 651-698 (2008). 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. Reviewer: A. Arvanitoyeorgos (Patras) MSC: 15A22 Matrix pencils 14E05 Rational and birational maps 14J26 Rational and ruled surfaces 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 PDFBibTeX XMLCite \textit{A. Coffman}, Electron. J. Linear Algebra 17, 651--698 (2008; Zbl 1173.15003) Full Text: DOI EuDML EMIS