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Abstract
Let R be a two-dimensional regular local ring with infinite residue field, and ℘ be a simple complete residually rational ideal of R of order r which determines R h . Let 𝒯 be the set of quadratic transforms T of R h with [T: R h ] = 1, and 𝒮 the set of simple complete ideals of R of order r which are adjacent to ℘ from below. If R h is free respectively a satellite, then there exist T* ∈ 𝒯 respectively T*, T** ∈ 𝒯 and a bijective map between the set 𝒮 and the set 𝒯∖{T*} respectively 𝒯∖{T*, T**}.
Notes
Communicated by I. Swanson.
1These notes shall be available on the first author's homepage http://math-www.uni-paderborn.de/ ∼karlh/Singularities, probably in May, 2010.