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.
The Milnor-Palamodov Theorem for Functions on Isolated Hypersurface Singularities
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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.
fields
math.AG 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
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.