Local systems on analytic germ complements

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• 作者：Nero Budur ; ^{Nero.Budur@wis.kuleuven.be} ; Botong Wang ^{botong.wang@wis.kuleuven.be}
• 关键词：Local systems ; Cohomology ; Jump loci ; Riemann&ndash ; Hilbert correspondence
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：14 January 2017
• 年：2017
• 卷：306
• 期：Complete
• 页码：905-928
• 全文大小：484 K
• 卷排序：306

文摘

We prove that the cohomology jump loci of rank one local systems on the complement in a small ball of a germ of a complex analytic set are finite unions of torsion translates of subtori. This is a generalization of the classical Monodromy Theorem stating that the eigenvalues of the monodromy on the cohomology of the Milnor fiber of a germ of a holomorphic function are roots of unity.