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摘要翻译：
通过多元Alexander多项式的棱镜，研究有限生成群的一次上同调跳跃轨迹中的余维一层。作为应用，我们给出了光滑拟射影复变体的基本群必须满足的新判据。这些判据精确地确定了复线排列的边界流形的哪些基本群是拟射影的。利用由Alexander多项式构造的多重性，给出了群的扭曲Betti秩的上界。对于同调3-球面中的Seifert链环，这些界变成了等式，我们的公式清楚地表明了Alexander多项式是如何决定所有特征变体的。
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英文标题：
《Alexander polynomials: Essential variables and multiplicities》
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作者：
Alexandru Dimca, Stefan Papadima, Alexander I. Suciu
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Group Theory 群论
分类描述：Finite groups, topological groups, representation theory, cohomology, classification and structure
有限群、拓扑群、表示论、上同调、分类与结构
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英文摘要：
We explore the codimension one strata in the degree-one cohomology jumping loci of a finitely generated group, through the prism of the multivariable Alexander polynomial. As an application, we give new criteria that must be satisfied by fundamental groups of smooth, quasi-projective complex varieties. These criteria establish precisely which fundamental groups of boundary manifolds of complex line arrangements are quasi-projective. We also give sharp upper bounds for the twisted Betti ranks of a group, in terms of multiplicities constructed from the Alexander polynomial. For Seifert links in homology 3-spheres, these bounds become equalities, and our formula shows explicitly how the Alexander polynomial determines all the characteristic varieties.
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PDF链接：
https://arxiv.org/pdf/0706.2499
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