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- W2890844368 abstract "The Milnor formula $mu=2delta-r+1$ relates the Milnor number $mu$, the double point number $delta$ and the number $r$ of branches of a plane curve singularity. It holds over the fields of characteristic zero. Melle and Wall based on a result by Deligne proved the inequality $mugeq 2delta-r+1$ in arbitrary characteristic and showed that the equality $mu=2delta-r+1$ characterizes the singularities with no wild vanishing cycles. In this note we give an account of results on the Milnor formula in characteristic $p$. It holds if the plane singularity is Newton non-degenerate (Boubakri et al. Rev. Mat. Complut. (2010) 25) or if $p$ is greater than the intersection number of the singularity with its generic polar (Nguyen H.D., Annales de l'Institut Fourier, Tome 66 (5) (2016)). Then we improve our result on the Milnor number of irreducible singularities (Bull. London Math. Soc. 48 (2016)). Our considerations are based on the properties of polars of plane singularities in characteristic $p$." @default.
- W2890844368 created "2018-09-27" @default.
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- W2890844368 date "2018-01-01" @default.
- W2890844368 modified "2023-09-23" @default.
- W2890844368 title "On the Milnor Formula in Arbitrary Characteristic" @default.
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- W2890844368 doi "https://doi.org/10.1007/978-3-319-96827-8_5" @default.
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