Hypersurface Complements, Alexander Modules and Monodromy

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dc.creatorDimca, A.
dc.creatorNemethi, A.
dc.date2002-01-29
dc.date.accessioned2026-07-07T04:46:11Z
dc.date.available2026-07-07T04:46:11Z
dc.descriptionWe consider an arbitrary polynomial map $f:{\mathbb C}^{n+1}\to {\mathbb C} $ and we study the Alexander invariants of ${\mathbb C}^{n+1}\setminus X$ 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.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/math/0201291
dc.identifierhttp://arxiv.org/abs/math/0201291
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63231
dc.subjectAlgebraic Geometry
dc.subject14J70, 14R25, 14D06, 32S40
dc.titleHypersurface Complements, Alexander Modules and Monodromy
dc.typetext

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