The Milnor-Palamodov Theorem for Functions on Isolated Hypersurface Singularities
classification
🧮 math.AG
keywords
hypersurfacenumberrelativebruce-robertsisolatedmilnor-palamodovproofsingularity
read the original abstract
In this note we give a simple proof of the following relative analog of the well known Milnor-Palamodov theorem: the Bruce-Roberts number of a function relative to an isolated hypersurface singularity is equal to its topological Milnor number (the rank of a certain relative (co)homology group) if and only if the hypersurface singularity is quasihomogeneous. The proof relies on an interpretation of the Bruce-Roberts number in terms of differential forms and the L\^e-Greuel formula.
This paper has not been read by Pith yet.
Forward citations
Cited by 1 Pith paper
-
The Bruce-Roberts number of a function on a hypersurface with isolated singularity
Proves μ_BR(f,X) = μ(f) + μ(φ,f) + μ(X,0) − τ(X,0) and that LC(X,0) is Cohen-Macaulay for isolated hypersurface singularities without assuming weighted homogeneity.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.