Degenerate real hypersurfaces in $\mathbb {C}^2$ with few automorphisms
Degenerate real hypersurfaces in $\mathbb {C}^2$ with few automorphisms
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$mathbb {C}^2$ 中的简并实超曲面，几乎没有自同构
DOI：
10.1090/s0002-9947-09-04626-1
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发表时间：
2006
影响因子：
1.3
通讯作者：
D. Zaitsev
中科院分区：
文献类型：
--
作者：
P. Ebenfelt;B. Lamel;D. Zaitsev
我们引入新的双全纯不变量的实解析超曲面在C2和展示如何使用它们来表明，超曲面拥有几个自同构。我们给的条件，在新的不变量，保证稳定组是有限的，并给（尖锐）界的基数的稳定组在这种情况下。我们还给出了稳定群为平凡群的一个充分条件。本文的主要技术工具是一个完整的（正式）规范形式的某一类超曲面。作为一个副产品，一个完整的分类，直到双全纯等价，有限型超曲面在这一类。
We introduce new biholomorphic invariants for real-analytic hypersurfaces in C 2 and show how they can be used to show that a hypersurface possesses few automorphisms. We give conditions, in terms of the new invariants, guaranteeing that the stability group is finite, and give (sharp) bounds on the cardinality of the stability group in this case. We also give a sufficient condition for the stability group to be trivial. The main technical tool developed in this paper is a complete (formal) normal form for a certain class of hypersurfaces. As a byproduct, a complete classification, up to biholomorphic equivalence, of the finite type hypersurfaces in this class is obtained.