A bound for the Milnor number of plane curve singularities

2013/05/22 by Arkadiusz Płoski, Płoski, Arkadiusz · 2 citations
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1305.5102

openalex publication_date 2013/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f=0 be a plane algebraic curve of degree d>1 with an isolated singular point at the origin of the complex plane. We show that the Milnor number μ₀(f) is less than or equal to (d-1)²-[(d)/(2)], unless f=0 is a set of d concurrent lines passing through 0. Then we characterize the curves f=0 for which μ₀(f)=(d-1)²-[(d)/(2)].

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