Classification of isolated hypersurface singularities by their moduli algebras
Classification of isolated hypersurface singularities by their moduli algebras
复制标题
DOI：
10.1007/bf01399504
复制
发表时间：
1982-06
影响因子：
3.1
通讯作者：
J. Mather;S. Yau
中科院分区：
文献类型：
--
作者：
J. Mather;S. Yau
证明了两个具有孤立奇点的复解析超曲面的芽是双全纯等价的当且仅当它们具有相同的维数且它们的模代数是同构的。这一结果在[1]中公布。文[1]中给出的例子表明，关于真实的数和关于特征p> 0的所有域的类似陈述都是错误的。w 1.孤立超曲面奇点的双全纯等价性设（5~+ 1）表示全纯函数（G”+ I，0）--C的原点芽环。设（V，0）是C”+ 1中超曲面的原点芽，设I（V）是C”+ 1中函数在V上为零的理想，f是I（V）的生成元. V-0是非奇异的当且仅当C-向量空间
We will prove that two germs of complex analytic hypersurfaces with isolated singularities are biholomorphically equivalent if and only if they have the same dimension and their moduli algebras are isomorphic. This result was announced in [1]. Examples given in [1] show that the analogous statements over the real numbers and over all fields of characteristic p> 0 are false. w 1. Biholomorphic Equivalence of Isolated Hypersurface SingularitiesLet (5~+ 1 denote the ring of germs at the origin of holomorphic functions (G"+ I, 0)--* C. If (V, 0) is a germ at the origin of a hypersurface in C"+ 1, let I (V) be the ideal of functions in 6;,+ 1 vanishing on V, and let f be a generator of I (V). It is well known that V-0 is non-singular if and only if the C-vector space