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Published online by Cambridge University Press: 16 September 2003
This paper gives an extension of the classical Zariski–van Kampen theorem describing the fundamental groups of the complements of plane singular curves by generators and relations. It provides a procedure for computation of the first non-trivial higher-homotopy groups of the complements of singular projective hypersurfaces in terms of the homotopy variation operators introduced here.
AMS 2000 Mathematics subject classification: Primary 14F35; 14D05; 32S20; 32S50. Secondary 14J70; 32S25; 55P99