On bifurcation braid monodromy of elliptic fibrations

Details On bifurcation braid monodromy of elliptic fibrations On bifurcation braid monodromy of elliptic fibrations

2004-10-12

arxiv.org/abs/math/0410295v1

Mathematics

Algebraic Geometry

17 pages, 2 figures

Scientific paper

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 I_1 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 I_1 fibres is at most 6.

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