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On the connectivity of some complete intersections

Alexandru Dimca
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Abstract

We show that the complement of a degree $d$ hypersurface in a projective complete intersection, whose defining equations have degrees strictly larger than $d$, has a rational connectivity higher than expected. The key new feature is that a positivity result replaces the usual transversality conditions needed to get such connectivity results.

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Alexandru Dimca. 2005-07-25. On the connectivity of some complete intersections. https://arxiv.org/abs/math/0507501

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