Abstract
Let π : X → T be a small deformation of a normal Gorenstein surface singularity X 0 = π-1(0) over the complex number field ℂ. Suppose that T is a neighborhood of the origin of ℂ and that X 0 is not log-canonical. We show that if a topological invariant -P t ⋅ P t of X t = π-1(t) is constant, then, after a suitable finite base change, π admits a simultaneous resolution f : M → X which induces a locally trivial deformation of each maximal string of rational curves at an end of the exceptional set of M 0 → X 0; in particular, if X 0 has a star-shaped resolution graph, then π admits a weak simultaneous resolution (in other words, π is an equisingular deformation).
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