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arXiv · 2605.21703

An algebraic proof of the Milnor-Orlik theorem

Yerly Soler
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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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Yerly Soler. 2026-05-20. An algebraic proof of the Milnor-Orlik theorem. https://doi.org/10.1007/s13366-026-00853-x

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