The Milnor number of plane irreducible singularities in positive characteristic
Abstract
Let μ(f) resp. c(f) be the Milnor number resp. the degree of the conductor of an irreducible power series f∈ [[x,y]], where is an algebraically closed field of characteristic p≥ 0. It is well-known that μ(f)≥ 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> f.
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