The Milnor number of plane irreducible singularities in positive characteristic

Abstract

\noindent Let $\mu (f)$ 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 $p\ge 0$. It is well-known that $\mu (f)\ge c(f)$. We give necessary and sufficient conditions for the equality $\mu (f)=c(f)$ in terms of the semigroup associated with $f$, provided that $p>\ord f$.

arXiv comment8 pages

References in corpus (1)

• Invariants of Hypersurface Singularities in Positive Characteristic

Cited by in corpus (1)

• On the Milnor formula in arbitrary characteristic