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

Mathematics – Algebraic Geometry

Scientific paper

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AMS-LaTeX, 13 pages

Scientific paper

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.

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