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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.
Unfolding CR Singularities
- MEMOIRS OF THE AMS
, 2010
"... A notion of unfolding, or multi-parameter deformation, of CR
singularities of real submanifolds in complex manifolds is proposed,
along with a definition of equivalence of unfoldings under the action
of a group of analytic transformations. In the case of real surfaces
in complex 2-space, deformatio ..."
Abstract
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Cited by 2 (1 self)
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A notion of unfolding, or multi-parameter deformation, of CR
singularities of real submanifolds in complex manifolds is proposed,
along with a definition of equivalence of unfoldings under the action
of a group of analytic transformations. In the case of real surfaces
in complex 2-space, deformations of elliptic, hyperbolic, and
parabolic points are analyzed by putting the parameter-dependent real
analytic defining equations into normal forms up to some order. For
some real analytic unfoldings in higher codimension, the method of
rapid convergence is used to establish real algebraic normal forms.
