Behavior of the Torsion of the Differential Module of an Algebroid Curve under Quadratic Transformations

Abstract

We study the difference between the lengths of the torsion of the differential modules of the local ring R of an algebroid curve and its first quadratic transform. The conjecture is that this difference should be positive if R is not regular. This is shown to be true in some cases, especially for stable complete intersections and for semigroup rings which are complete intersections.