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Zbl 1020.32025
Artal Bartolo, E.; Cassou-Noguès, P.; Luengo, I.; Melle Hernández, A.
Monodromy conjecture for some surface singularities. (English)
[J] Ann. Sci. Éc. Norm. Supér. (4) 35, No. 4, 605-640 (2002). ISSN 0012-9593

Summary: We give a formula for the local Denef-Loeser zeta function of a superisolated singularity of hypersurface in terms of the local Denef-Loeser zeta function of the singularities of its tangent cone. We prove the monodromy conjecture for some surface singularities. These results are applied to the study of rational arrangements of plane curves whose Euler-Poincaré characteristic is three.

MSC 2000:: *32S50 Topological aspects with respect to singularities on analytic spaces
32S25 (Hyper-) Surface singularities (analytic spaces)
14B05 Singularities (algebraic geometry)
14E15 Global theory of singularities

Keywords: topological zeta function; monodromy conjecture; local Denef-Loeser zeta function; superisolated singularity of hypersurface; rational arrangements of plane curves

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