On the fundamental groups of normal varieties (Q2809267)

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scientific article; zbMATH DE number 6586437
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On the fundamental groups of normal varieties
scientific article; zbMATH DE number 6586437

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    On the fundamental groups of normal varieties (English)
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    27 May 2016
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    normal varieties
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    fundamental groups
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    local systems
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    twisted cohomology
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    resonance varieties
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    characteristic varieties
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    Malcev Lie algebras, Hodge structure
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    The goal of the paper under review is ``to give some evidence that the fundamental groups of normal varieties behave like those of smooth varieties''. In particular, the authors generalize a main theorem from [\textit{D. Arapura}, J. Algebr. Geom. 6, No. 3, 563--597 (1997; Zbl 0923.14010)] and describe the jump loci phenomenon of rank one local systems on an irreducible normal variety \(X\) using the resonance and characteristic varieties of \(X\) and its resolution [\textit{A. Dimca} et al., Duke Math. J. 148, No. 3, 405--457 (2009; Zbl 1222.14035)]. They also give a detail proof of the well-known Deligne's statement that Morgan's theorem holds for normal varieties, obtain an analog of Theorem 11.7 [loc. cit.] concerning conditions under which a right-angled Artin group is the fundamental group of a normal variety, etc. In conclusion the authors remark that ``it would be interesting to find an example of a group which is the fundamental group of a normal variety but not the fundamental group of a smooth variety''.
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