Analytic Normal Form for CR Singular Surfaces
نویسنده
چکیده
A real analytic surface inside complex 3-space with an isolated, nondegenerate complex tangent is shown to be biholomorphically equivalent to a fixed real algebraic variety. The analyticity of the normalizing transformation is proved using a rapid convergence argument. Real surfaces in higher dimensions are also shown to have an algebraic normal form. 1 2
منابع مشابه
Real Submanifolds of Maximum Complex Tangent Space at a Cr Singular Point, I
We study a germ of real analytic n-dimensional submanifold of C that has a complex tangent space of maximal dimension at a CR singularity. Under some assumptions, we show its equivalence to a normal form under a local biholomorphism at the singularity. We also show that if a real submanifold is formally equivalent to a quadric, it is actually holomorphically equivalent to it, if a small divisor...
متن کاملCr Singularities of Real Threefolds in C
CR singularities of real threefolds in C4 are classified by using holomorphic coordinate changes to transform the quadratic part of the real defining equations into one of a list of normal forms. In the non-degenerate case, it is shown that a real analytic manifold near a CR singular point is formally equivalent to a real algebraic model. Some degenerate cases also have this property.
متن کاملSolvability of infinite system of nonlinear singular integral equations in the C(Itimes I, c) space and modified semi-analytic method to find a closed-form of solution
In this article, we discuss about solvability of infinite systems of singular integral equations with two variables in the Banach sequence space $C(I times I, c)$ by applying measure of noncompactness and Meir-Keeler condensing operators. By presenting an example, we have illustrated our results. For validity of the results we introduce a modified semi-analytic method in the case of tw...
متن کاملA Codimension Two CR Singular Submanifold That Is Formally Equivalent to a Symmetric Quadric
Let M ⊂ Cn+1 (n ≥ 2) be a real analytic submanifold defined by an equation of the form: w = |z|2 + O(|z|3), where we use (z,w) ∈ C × C for the coordinates of Cn+1. We first derive a pseudo-normal form for M near 0. We then use it to prove that (M, 0) is holomorphically equivalent to the quadric (M∞ : w = |z|2, 0) if and only if it can be formally transformed to (M∞, 0). We also use it to give a...
متن کاملAutomorphism Groups on Normal Singular Cubic Surfaces with No Parameters
The classification of normal singular cubic surfaces in P3 over a complex number field C was given by J. W. Bruce and C. T. C. Wall. In this paper, first we prove their results by a different way, second we provide normal forms of normal singular cubic surfaces according to the type of singularities, and finally we determine automorphism groups on normal singular cubic surfaces with no parameters.
متن کامل