Universal abelian covers of certain surface singularities
Universal abelian covers of certain surface singularities
复制标题
DOI：
10.1007/s00208-005-0693-8
复制
发表时间：
2005-03
影响因子：
1.4
通讯作者：
Tomohiro Okuma
中科院分区：
文献类型：
--
作者：
Tomohiro Okuma
每一个具有同调球环的法线复曲面奇点都有一个泛阿贝尔覆盖。Neumann和Wahl猜想，有理奇点或极小椭圆奇点的泛阿贝尔覆盖是由“拼接图方程组”定义的完全交奇点。本文引入了一个类似于拼接图方程组的Neumann-Wahl系，证明了：如果(X，o)是有理或极小椭圆奇点，则它的泛阿贝尔覆盖(Y，o)是由Neumann-Wahl系定义的孤立完全交奇点(Y0，o)的等角形变.此外，如果G表示覆盖Y→X的伽罗瓦群，则G也作用于Y0，X是商Y0/G的等值变形。
Every normal complex surface singularity with -homology sphere link has a universal abelian cover. It has been conjectured by Neumann and Wahl that the universal abelian cover of a rational or minimally elliptic singularity is a complete intersection singularity defined by a system of ``splice diagram equations''. In this paper we introduce a Neumann-Wahl system, which is an analogue of the system of splice diagram equations, and prove the following.If (X, o) is a rational or minimally elliptic singularity, then its universal abelian cover (Y, o) is an equisingular deformation of an isolated complete intersection singularity (Y0,o) defined by a Neumann-Wahl system. Furthermore, ifGdenotes the Galois group of the coveringY→X, thenGalso acts onY0andXis an equisingular deformation of the quotientY0/G.