On the connectivity of some complete intersections

Details On the connectivity of some complete intersections On the connectivity of some complete intersections

2005-07-25

arxiv.org/abs/math/0507501v1

in: The second Japanese-Australian Workshop on Real and Complex Singularities, RIMS K\^oky\^uroku 1610, pp.11-17(2008).

Mathematics

Algebraic Geometry

Scientific paper

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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