The Milnor-Palamodov Theorem for Functions on Isolated Hypersurface Singularities
Algebraic Geometry
2018-11-20 v1
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.
Keywords
Cite
@article{arxiv.1811.07422,
title = {The Milnor-Palamodov Theorem for Functions on Isolated Hypersurface Singularities},
author = {Konstantinos Kourliouros},
journal= {arXiv preprint arXiv:1811.07422},
year = {2018}
}