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arXiv · 1202.0844

L^2-Betti numbers of hypersurface complements

Laurentiu Maxim
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Abstract

In \cite{DJL07} it was shown that if $\scra$ is an affine hyperplane arrangement in $\C^n$, then at most one of the $L^2$--Betti numbers $b_i^{(2)}(\C^n\sm \scra,\id)$ is non--zero. In this note we prove an analogous statement for complements of complex affine hyperurfaces in general position at infinity. Furthermore, we recast and extend to this higher-dimensional setting results of \cite{FLM,LM06} about $L^2$--Betti numbers of plane curve complements.

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Laurentiu Maxim. 2012-04-09. L^2-Betti numbers of hypersurface complements. https://doi.org/10.1093/imrn%2Frnt093

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