An algebraic proof of the Milnor-Orlik theorem
Commutative Algebra
2026-05-22 v1
Abstract
A well-known theorem by Milnor-Orlik provides a formula for the Milnor number of a weighted-homogeneous polynomial having an isolated singularity that depends only on the weights. In this paper we present a proof of that result using techniques from commutative algebra. Our approach is to obtain a free resolution of the Milnor algebra through the Koszul complex. The desired formula is then obtained from a Hilbert series calculation.
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Cite
@article{arxiv.2605.21703,
title = {An algebraic proof of the Milnor-Orlik theorem},
author = {Yerly Soler},
journal= {arXiv preprint arXiv:2605.21703},
year = {2026}
}
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5 pages