On bifurcation braid monodromy of elliptic fibrations

2004/10/12 by Michael Lönne, Lönne, Michael · 1 citation
Mathematics · #14D05 #14J27 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14D05 #msc:14J27

paper · pdf · doi:10.48550/arxiv.math/0410295

17 pages, 2 figures

arxiv created 2004/10/12 · arxiv updated 2009/12/01

Abstract

We define a monodromy homomorphism for irreducible families of regular elliptic fibrations which takes values in the mapping class group of a punctured sphere. We compute the monodromy for elliptic fibrations only which contain no singular fibres of types other than I₁ and I*₀. There are maximal groups, which can be the monodromy groups of algebraic, resp. differentiable families of elliptic surfaces, and we give an algebraic criterion for the equality of both groups which we can check to apply in case the number of I₁ fibres is at most 6.

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