The homology of generalized Brieskorn manifolds
The homology of generalized Brieskorn manifolds
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广义 Brieskorn 流形的同调
DOI：
10.1016/0040-9383(75)90019-1
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发表时间：
1975
期刊：
影响因子：
--
通讯作者：
R. Randell
中科院分区：
文献类型：
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作者：
R. Randell
51.引言在本文中，我们给出了一个算法的证明，用于计算由Brieskorn品种的完全交叉定义的流形的同调。特别地，我们证明了Orlik [7]关于Brieskorn流形的同调挠率的算法.我们还计算了这类流形上某个S '-作用的轨道空间的同调。令fi（Z，r.，tn+ m（n+ m）= F，i，z，n，i= 1，.，171是复多项式的集合。设V= fi Vi，其中Vi是fi的零点的轨迹。其中i=，di= 1。cm（all，.，ai，.+，）且qir= dilaii，我们假设（i）V是Vi的完全交。(ii)V在原点有一个孤立的奇点。(iii)Qij独立于i。(and因此我们定义qi= q+）如果（i）、（ii）、（iii）成立，我们将说V是广义Brieskorn簇，并且
51. INTRODUCTION IN THIS paper we give a proof of an algorithm for computing the homology of manifolds defined by complete intersections of Brieskorn varieties. In particular we prove the algorithm conjectured by Orlik [7] for the homology torsion of Brieskorn manifolds. We also compute the homology of the orbit space of a certain S’-action on these manifolds. Let fi (Z, r..., tn+ m n+ m)= F, oijz,““, i= l,..., 171 be a collection of complex polynomials. Let V= fi Vi, where Vi is the locus of zeroes of fi. With i=, di= 1. cm (ail,..., ai,.+,) and qir= dilaii we suppose (i) V is the complete intersection of the Vi.(ii) V has an isolated singularity at the origin.(iii) qij is independent of i.(and so we define qi= q+) If (i),(ii),(iii) hold, we will say that V is a generalized Brieskorn variety and