The Milnor fiber of the singularity f(x,y) + zg(x,y) = 0

2014/11/05 by Sigurðsson, Baldur
#32S05 #32S25 #32S55 #32Sxx (Secondary) #58K10 (Primary) 14Bxx #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1411.1298

Abstract

We give a description of the Milnor fiber and the monodromy of a singularity of the form f+zg = 0 where f and g define plane curves and have no common components. The description depends only on the topological type of the two plane curve germs defined by f and g. In particular, this gives a description of the boundary of the Milnor fiber. As a corollary, we give a simple formula for the monodromy zeta function and the Euler characteristic of the fiber.

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