2002/01/29 by A. Dimca, Dimca, A., A. Nemethi +1
Mathematics · #14D06 #14J70 #14R25 #32S40 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14D06 #msc:14J70 #msc:14R25 #msc:32S40
paper · pdf · doi:10.48550/arxiv.math/0201291
22 pages
arxiv created 2002/01/29 · arxiv updated 2009/11/30
We consider an arbitrary polynomial map f:\mathbb Cn+1→ \mathbb C and we study the Alexander invariants of \mathbb Cn+1∖ X for any fiber X of f. The article has two major messages. First, the most important qualitative properties of the Alexander modules are completely independent of the behaviour of f at infinity, or about the special fibers. Second, all the Alexander invariants of all the fibers of the polynomial f are closely related to the monodromy representation of f. In fact, all the torsion parts of the Alexander modules (associated with all the possible fibers) can be obtained by factorization of a unique universal Alexander module, which is constructed from the monodromy representation. Additionally, the article extends some results of A. Libgober about Alexander modules of hypersurface complements.