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arXiv · 1505.07075

The Milnor number of plane irreducible singularities in positive characteristic

Evelia R. García Barroso·Arkadiusz Płoski
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Abstract

\noindent Let $μ(f)$ resp. $c(f)$ be the Milnor number resp. the degree of the conductor of an irreducible power series $f\in \bK[[x,y]]$, where $\bK$ is an algebraically closed field of characteristic $p\geq 0$. It is well-known that $μ(f)\geq c(f)$. We give necessary and sufficient conditions for the equality $μ(f)=c(f)$ in terms of the semigroup associated with $f$, provided that $p>\ord f$.

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Evelia R. García Barroso, Arkadiusz Płoski. 2015-06-05. The Milnor number of plane irreducible singularities in positive characteristic. https://doi.org/10.1112/blms%2Fbdv095

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