Intersection homology and Alexander modules of hypersurface complements

@article{Maxim2004IntersectionHA,
  title={Intersection homology and Alexander modules of hypersurface complements},
  author={Laurenţiu Maxim},
  journal={Commentarii Mathematici Helvetici},
  year={2004},
  volume={81},
  pages={123-155}
}
  • L. Maxim
  • Published 21 September 2004
  • Mathematics
  • Commentarii Mathematici Helvetici
Let $V$ be a degree $d$, reduced hypersurface in $\mathbb{CP}^{n+1}$, $n \geq 1$, 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 of the total linking number homomorphism. Using intersection homology theory, we give a new construction of the Alexander modules $H_i(\mathcal{U}^c;\mathbb{Q})$ of the hypersurface… 
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