Holomorphic Equivalence and Nonlinear Symmetries of Ruled Hypersurfaces in C2

被引：0

作者：

Kolar, Martin ^{[1
]}

Lamel, Bernhard ^{[2
]}

机构：

[1] Masaryk Univ, Dept Math & Stat, Brno, Czech Republic

[2] Univ Vienna, Fac Math, Vienna, Austria

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2015年 / 25卷 / 02期

关键词：

Infinite type; Ruled hypersurfaces; Local equivalence problem; Normal forms; Nonlinear automorphisms;

D O I：

10.1007/s12220-013-9465-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We solve the local equivalence problem for ruled hypersurfaces in C-2 at a point of infinite type by giving a normal form. We describe all ruled hypersurfaces which admit nonlinear symmetries and give their complete characterization according to the dimension of their automorphism group. As an application, we give a bound for the dimension of the stability group for a family of nonminimal hypersurfaces.

引用

页码：1240 / 1281

页数：42

共 50 条

[41] Interpolation by proper holomorphic embeddings of the disc into C2
Globevnik, J
MATHEMATICAL RESEARCH LETTERS, 2002, 9 (04) : 567 - 577
[42] Equivalence of polynomials under automorphisms of C2
Wightwick, PG
JOURNAL OF PURE AND APPLIED ALGEBRA, 2001, 157 (2-3) : 341 - 367
[43] ON THE LOCALLY BIHOLOMORPHIC EQUIVALENCE OF SMOOTH HYPERSURFACES IN C-2
ABROSIMOV, AV
DOKLADY AKADEMII NAUK SSSR, 1988, 299 (04): : 777 - 781
[44] The Nonlinear Boundary Value Problem for k Holomorphic Functions in DOUBLE-STRUCK CAPITAL C2
Cui, Yanyan
Li, Zunfeng
Xie, Yonghong
Qiao, Yuying
ACTA MATHEMATICA SCIENTIA, 2023, 43 (04) : 1571 - 1586
[45] ON THE REAL-ANALYTICITY OF RIGID SPHERICAL HYPERSURFACES IN C2
Isaev, Alexander
Merker, Joel
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 147 (12) : 5251 - 5256
[46] A SHORT PROOF OF THE DIMENSION CONJECTURE FOR REAL HYPERSURFACES IN C2
Isaev, Alexander
Kruglikov, Boris
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144 (10) : 4395 - 4399
[47] Holomorphic equivalence between basins of attraction in C-2
Berteloot, F
Loeb, JJ
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1996, 45 (02) : 583 - 589
[48] THE CONTINUITY OF REDUCTION OF HYPERSURFACES IN C2 TO A NORMAL-FORM
LOBODA, AV
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1993, 27 (04) : 288 - 290
[49] A holomorphic extension theorem from a fractal hypersurface in C2
Abreu Blaya, Ricardo
Bory Reyes, Juan
Moreno Garcia, Tania
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2007, 38 (04): : 635 - 647
[50] Holomorphic motions and structural stability for polynomial automorphisms of C2
Buzzard, Gregery T.
Jenkins, Adrian
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2008, 57 (01) : 277 - 308

← 1 2 3 4 5 →