2009/09/02 by András Némethi, Andras Nemethi, Nemethi, Andras +3 · 3 citations
Mathematics · #14B05 #14J17 #14P15 #32S05 #32S22 #32S25 (Primary) #32S35 #32S40 #32S45 #32S55 #57M27 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14B05 #msc:14J17 #msc:14P15 #msc:32S05 #msc:32S22 #msc:32S25 #msc:32S35 #msc:32S40 #msc:32S45 #msc:32S55 #msc:57M27
paper · pdf · doi:10.48550/arxiv.0909.0354
232 pages
openalex publication_date 2009/09/02 · arxiv created 2011/06/22 · arxiv updated 2011/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let f be a hypersurface surface local singularity whose zero set has 1-dimensional singular locus. We develop an explicit procedure that provides the boundary of the Milnor fibre of f as an oriented plumbed 3-manifold. The method provides the characteristic polynomial of the algebraic monodromy as well. Moreover, for any analytic germ g such that the pair (f,g) is an isolated complete intersection singularity, the (multiplicity system of the) open book decomposition of the boundary with binding determined by g and pages determined by the argument of g is also computed. In order to do this, we have to establish key results regarding the horizontal and vertical monodromies of the transversal type singularities associated with the singular locus of f and of the ICIS (f,g). The theory is supported by many examples. E.g. the case of homogeneous singularities (including the case of arrangements) is detailed completely. A list of especially peculiar examples, and also a list of related open problems is given.