一类伪加权射影平面的整体向量场及其局部指标
Global vector fields and their local indices on a class of fake weighted projective planes
辛赫 1闫冰清1
作者信息
- 1. 渤海大学数学科学学院,辽宁锦州 121013
- 折叠
摘要
给出了四个带有奇点的Gorenstein伪加权射影平面上的所有的整体切向量场,并利用推广的Poincaré-Hopf定理,证明了这些曲面上一些特征整体向量场在每一个奇点处的GSV-指标都等于1+μ,其中μ为该奇点的Milnor数.与光滑流形不同,奇异解析簇上具有孤立零点的向量场的局部指标一般不易计算.在此方面提供了一个具体实例.
Abstract
We give all the global tangent vector fields on four Gorenstein fake weighted projective planes with singularities,and by making use of the generalized Poincaré-Hopf theorem we prove the GSV-indices for some characteristic global vector fields at each of the singularities on these surfaces are equal to 1+μ,where μ is the Milnor number of the singularity.Unlike the smooth manifolds case,the computation of local indices for vector fields with isolated zeros on singular analytic varieties is difficult in general.Our work provides a concrete example with respect to this issue.
关键词
伪加权射影平面/整体切向量场/GSV-指标Key words
fake weighted projective planes/global tangent vector fields/GSV-indices引用本文复制引用
出版年
2024
NETL
NSTL
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