| Popis: |
The question, whether the torsion submodule Τ of the differential module of the local ring R of a singular point of an algebraic or algebroid curve is not zero, is still open in general. All examples suggest the conjecture that this torsion genuinely decreases when going from R to the first quadratic transform R 1, which would imply that Τ was nontrivial in the first place. We give a general formula for the difference \( \ell _R (T) - \ell _{R_1 } (T_1 )\) of the lengths of these torsions. In the special cases that R is a semigroup ring which is a complete intersection or that R is a “nice” almost complete intersection or a “stable” complete intersection (definition 1) the conjecture is proved. |
