A hyperplane section theorem for Milnor numbers
We prove the following result. Theorem. Let \(R\) denote the power series ring \(\mathbb{C} X_1,X_2, \dots, X_n\) and \(f\in R\) any irreducible element. Assume that for any element \(h\in R\) which is a part of a minimal system of generators of the maximal ideal of \(R\) the ring \(R/(f,h)\) has an isolated singular point. Then the set of Milnor numbers of the rings \(R/(f,h)\) with any \(h\) as above is bounded above. The converse of this result is also true and it was observed by A. J. Parameswaran.
intersection multiplicity of plane curves
scientific article; zbMATH DE number 1121710