Die monodromie der isolierten singularitäten von hyperflächen
Die monodromie der isolierten singularitäten von hyperflächen
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超薄层的单一单一性
DOI：
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发表时间：
1970
期刊：
影响因子：
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通讯作者：
E. Brieskorn
中科院分区：
文献类型：
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作者：
E. Brieskorn
J. Milnor最近介绍了超曲面的孤立奇点的局部Picard-Lefschetz-monodromy。这是研究奇点拓扑的一个重要工具。单值性是作用在某个上同调群上的一种作用，它是用拓扑术语定义的。在本文中，我们找到一个代数描述的monodromy。用代数方法构造了一个正则奇异常线性微分算子，使得该奇异算子的单值性与Picard-Lefschetz单值性一致.作为应用，我们证明了monodromy的特征值是单位根。我们的处理在精神上接近于格罗滕迪翁的高β-马宁联系理论。
J. Milnor recently introduced the local Picard-Lefschetz-monodromy of an isolated singularity of a hypersurface. This is an important tool in the investigation of the topology of singularities. The monodromy is an action on a certain cohomology group and is defined in topological terms. In this paper we find an algebraic description of the monodromy. We construct by algebraic methods a regular singular ordinary linear differential operator, such that the monodromy of this singular operator coincides with the Picard-Lefschetz monodromy. As an application we prove that the eigenvalues of the monodromy are roots of unity. Our treatment is close in spirit to Grothendiecks theory of the Gauβ-Manin-connection.