ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: 14, 57 Balke, Ludwig, Universität Bonn, Germany Open book fibrations of lens spaces and deformations of cyclic quotient singularities. Let X = ℂ^{2}/Γ with Γ a cyclic group of order n and z_{1} = x^{n} ∈ ℂ[x, y] a Γ-invariant. The link L = S^{3}/Γ of the the cyclic quotient singularity 0 ∈ X is a lens space and z_{1}/|z_{1}| yields an open book fibration of L. For a deformation X_{t} of X, the function z_{1} is holomorphic on X_{t} and we obtain a diffeomorphism from L to a 3-manifold L_{t} ⊂ X_{t}. Moreover, L_{t} is provided with an open-book fibration by the function z_{1}/|z_{1}|. We show, that there is a correspondence between the components of the base of the miniversal deformation of X and isotopy classes of such open book fibrations. That means, the different components of the base have a topological reason.