Hypersurface complements, Milnor fibers and minimality of arrangements

Details Hypersurface complements, Milnor fibers and minimality of arrangements Hypersurface complements, Milnor fibers and minimality of arrangements

2000-11-27

arxiv.org/abs/math/0011222v2

Mathematics

Algebraic Topology

12 pages

Scientific paper

We describe a new relation between the topology of hypersurface complements, Milnor fibers and degree of gradient mappings. The main tools are polar curves and the affine Lefschetz theory developped by H. Hamm and A. N\'emethi. In the special case of the hyperplane arrangements, we strengthen some results due to Orlik and Terao (see Math. Ann. 301(1995)) and obtain an independant proof for the minimality of hyperplane arrangements (see Randell math.AT/0011101 for another proof of this result).

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