Example of a noncontinuable holomorphic transformation of an analytic hypersurface

1982 ◽  
Vol 32 (1) ◽  
pp. 540-541 ◽  
Author(s):  
V. K. Beloshapka
Keyword(s):  
Analytic Hypersurface ◽  
Holomorphic Transformation

A Remark on the Tautness modulo an Analytic Hypersurface of Hartogs-Type Domains

2020 ◽  
Vol 72 (1) ◽  
pp. 136-148
Author(s):  
D. T. Pham
Keyword(s):  
Analytic Hypersurface

scholarly journals Local algebraicity of some analytic hypersurface

1980 ◽  
Vol 79 (4) ◽  
pp. 546-546
Author(s):  
William A. Adkins
Keyword(s):  
Analytic Hypersurface

ON THE MULTIPLICITIES OF FAMILIES OF COMPLEX HYPERSURFACE-GERMS WITH CONSTANT MILNOR NUMBER

2013 ◽  
Vol 24 (03) ◽  
pp. 1350021 ◽  
Author(s):  
CAMILLE PLENAT ◽  
DAVID TROTMAN
Keyword(s):  
Tangent Cone ◽  
Milnor Number ◽  
Analytic Family ◽  
Singular Set ◽  
Analytic Hypersurface ◽  
Hypersurface Singularities

We show that the possible drop in multiplicity in an analytic family F(z, t) of complex analytic hypersurface singularities with constant Milnor number is controlled by the powers of t. We prove equimultiplicity of μ-constant families of the form f + tg + t2h if the singular set of the tangent cone of {f = 0} is not contained in the tangent cone of {h = 0}.

scholarly journals Fixed points of elliptic reversible transformations with integrals

1996 ◽  
Vol 16 (4) ◽  
pp. 683-702
Author(s):  
Xianghong Gong
Keyword(s):  
Normal Form ◽  
Fixed Points ◽  
Periodic Points ◽  
General Transformation ◽  
Reversible Transformation ◽  
Level Curves ◽  
Hyperbolic Complex ◽  
Holomorphic Transformation ◽  
Real Analytic ◽  
Real Hyperplane

AbstractWe show that for a certain family of integrable reversible transformations, the curves of periodic points of a general transformation cross the level curves of its integrals. This leads to the divergence of the normal form for a general reversible transformation with integrals. We also study the integrable holomorphic reversible transformations coming from real analytic surfaces in ℂ2 with non-degenerate complex tangents. We show the existence of real analytic surfaces with hyperbolic complex tangents, which are contained in a real hyperplane, but cannot be transformed into the Moser—Webster normal form through any holomorphic transformation.

scholarly journals On algebraic representatives of topological types of analytic hypersurface germs

2012 ◽  
Vol 21 (4) ◽  
pp. 789-797 ◽  
Author(s):  
Javier Fernández de Bobadilla
Keyword(s):  
Analytic Hypersurface

scholarly journals On Propagation of Sphericity of Real Analytic Hypersurfaces across Levi Degenerate Loci

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Joël Merker
Keyword(s):  
Open Subset ◽  
Levi Form ◽  
Dense Open Subset ◽  
Real Analytic Hypersurface ◽  
Analytic Hypersurface ◽  
Real Analytic ◽  
Real Analytic Hypersurfaces

A connected real analytic hypersurface M⊂Cn+1 whose Levi form is nondegenerate in at least one point—hence at every point of some Zariski-dense open subset—is locally biholomorphic to the model Heisenberg quadric pseudosphere of signature (k,n-k) in one point if and only if, at every other Levi nondegenerate point, it is also locally biholomorphic to some Heisenberg pseudosphere, possibly having a different signature (l,n-l). Up to signature, pseudosphericity then jumps across the Levi degenerate locus and in particular across the nonminimal locus, if there exists any.

Example of a real-analytic hypersurface with nonlinearizable stability group

1988 ◽  
Vol 44 (5) ◽  
pp. 824-828 ◽  
Author(s):  
V. V. Ezhov
Keyword(s):  
Stability Group ◽  
Real Analytic Hypersurface ◽  
Analytic Hypersurface ◽  
Real Analytic

Holomorphic Transformation to a Miniversal Deformation not Always Exists Under *Congruence

2015 ◽  
Vol 66 (9) ◽  
pp. 1431-1434
Author(s):  
O. M. Klymenko
Keyword(s):  
Holomorphic Transformation
Sign in / Sign up

Export Citation Format

Share Document