Hypersurface complements, Milnor fibers and minimality of arrangements

2000/11/27 by Alexandru Dimca, A. Dimca, Dimca, A.
Mathematics · #14D05 #14F25 #52C35 #55Q52 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #math.AT #msc:14D05 #msc:14F25 #msc:52C35 #msc:55Q52

paper · pdf · doi:10.48550/arxiv.math/0011222

12 pages

openalex publication_date 2000/11/27 · arxiv created 2000/12/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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. Némethi. 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).

Citations

• Higher Homotopy Groups of Complements of Complex Hyperplane Arrangements

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