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Real congruence of complex matrix pencils and complex projections of real Veronese varieties
- Linear Algebra and its Applications
, 2003
"... Quadratically parametrized maps from a real projective space to a
complex projective space are constructed as projections of the
Veronese embedding. A classification theorem relates equivalence
classes of projections to real congruence classes of complex symmetric
matrix pencils. The images of som ..."
Abstract
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Cited by 6 (6 self)
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Quadratically parametrized maps from a real projective space to a
complex projective space are constructed as projections of the
Veronese embedding. A classification theorem relates equivalence
classes of projections to real congruence classes of complex symmetric
matrix pencils. The images of some low-dimensional cases include
certain quartic curves in the Riemann sphere, models of the real
projective plane in complex projective 4-space, and some normal form
varieties for real submanifolds of complex space with CR
singularities.
Analytic stability of the CR cross-cap
- Pacific Journal of Mathematics
, 2006
"... For m
Abstract
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Cited by 2 (2 self)
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For m<n, any real analytic m-submanifold of complex n-space with a
nondegenerate CR singularity is shown to be locally equivalent, under
a holomorphic coordinate change, to a fixed real algebraic variety
defined by linear and quadratic polynomials. The situation is
analogous to Whitney's stability theorem for cross-cap singularities
of smooth maps. The complex analyticity of the normalizing
transformation is proved using a rapid convergence argument.
Real equivalence of complex matrix pencils and complex projections of real Segre varieties
- Electronic Journal of Linear Algebra
, 2008
"... Abstract. Quadratically parametrized maps from a product of real projective spaces to a complex projective space are constructed as the composition of the Segre embedding with a projection. A classification theorem relates equivalence classes of projections to equivalence classes of complex matrix p ..."
Abstract
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Cited by 1 (1 self)
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Abstract. Quadratically parametrized maps from a product of real projective spaces to a complex projective space are constructed as the composition of the Segre embedding with a projection. 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, and some of these images exhibit CR singularities.
CR SINGULARITIES OF REAL FOURFOLDS IN C3
- ILLINOIS JOURNAL OF MATHEMATICS
, 2009
"... CR singularities of real 4-submanifolds in complex 3-space are classified by using local holomorphic coordinate changes to transform the quadratic coefficients of the real analytic defining equation into a normal form. The quadratic coefficients determine an intersection index, which appears in glob ..."
Abstract
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CR singularities of real 4-submanifolds in complex 3-space are classified by using local holomorphic coordinate changes to transform the quadratic coefficients of the real analytic defining equation into a normal form. The quadratic coefficients determine an intersection index, which appears in global enumerative formulas for CR singularities of compact submanifolds.
