Generic linear sections of complex hypersurfaces and monomial ideals
Let \(f:(\mathbb{C}^{n},0)\rightarrow (\mathbb{C},0)\) be an analytic function germ with an isolated singularity at the origin. Let \(\mu ^{\ast }(f)=\big(\mu ^{(n)}(f),\dots ,\mu ^{(i)}(f),\dots ,\mu ^{\left( 0\right) }(f)\big)\) be the sequence of Milnor numbers of the restriction of \(f\) to a generic plane in \( \mathbb{C}^{n}\) of dimension \(i.\) So, \(\mu ^{(n)}(f)=\mu (f)\) is the standard Milnor number of \(f,\) \(\mu ^{(1)}(f)=\text{ord}f-1\) and \(\mu ^{(0)}(f)=1.\) The author gives an expression for the sequence \(\mu ^{\ast }(f)\) in terms of the Newton polyhedron of \(f\) under the condition that \(f\) is non-degenerate (the famous Kouchnirenko formula gives an expression for \( \mu ^{(n)}(f)\) only).
scientific article; zbMATH DE number 6011292
scientific article