An algebraic proof of the Milnor-Orlik theorem
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917518185070592 |
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| author | Soler, Yerly |
| author_facet | Soler, Yerly |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21703 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An algebraic proof of the Milnor-Orlik theorem Soler, Yerly Commutative Algebra 14B05, 32S25, 13D02, 13D40 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. |
| title | An algebraic proof of the Milnor-Orlik theorem |
| topic | Commutative Algebra 14B05, 32S25, 13D02, 13D40 |
| url | https://arxiv.org/abs/2605.21703 |