Let $V$ be a degree $d$, reduced hypersurface in $\mathbb{CP}^{n+1}$, $n \geq1$, and fix a generic hyperplane, $H$. Denote by $\mathcal{U}$ the (affine)hypersurface complement, $\mathbb{CP}^{n+1}- V \cup H$, and let $\mathcal{U}^c$be the infinite cyclic covering of $\mathcal{U}$ corresponding to the kernel ofthe linking number homomorphism. Using intersection homology theory, we give anew construction of the Alexander modules $H_i(\mathcal{U}^c;\mathbb{Q})$ ofthe hypersurface complement and show that, if $i \leq n$, these are torsionover the ring of rational Laurent polynomials. We also obtain obstructions onthe associated global polynomials. Their zeros are roots of unity of order $d$and are entirely determined by the local topological information encoded by thelink pairs of singular strata of a stratification of the pair$(\mathbb{CP}^{n+1},V)$. As an application, we give obstructions on theeigenvalues of monodromy operators associated to the Milnor fibre of aprojective hypersurface arrangement.
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机译：假设$ V $为度数$ d $，减少$ \ mathbb {CP} ^ {n + 1} $，$ n \ geq1 $中的超曲面，并修复通用超平面$ H $。用$ \ mathcal {U} $表示（仿射）超曲面补，$ \ mathbb {CP} ^ {n + 1}-V \ cup H $，并将$ \ mathcal {U} ^ c $设为无限循环$ \ mathcal {U} $的覆盖范围，对应于链接数同态的核。使用相交同源性理论，我们给出超曲面补的亚历山大模块$ H_i（\ mathcal {U} ^ c; \ mathbb {Q}）$的新构造，并证明，如果$ i \ leq n $，则它们在Laurent多项式的环。我们还获得了相关联的全局多项式的障碍。它们的零是单位d $$的单位根，并且完全由对成对$（\ mathbb {CP} ^ {n + 1}，V）$的奇异层的链接对编码的局部拓扑信息确定。 。作为一种应用，我们对与投影超表面排列的米尔诺纤维有关的单峰算子的特征值给出了障碍。
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