2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76913We 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.AMS-LaTeX, 13 pagesAlgebraic GeometryCommutative Algebra13N05 (Primary) 13B10, 14F10 (Secondary)text